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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 371280.cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 371280.cy1 | 371280cy7 | \([0, -1, 0, -36136447040, 2644041474756480]\) | \(1274090022584975661628188489514561/14072533302105480763470\) | \(57641096405424049207173120\) | \([4]\) | \(603979776\) | \(4.5125\) | |
| 371280.cy2 | 371280cy5 | \([0, -1, 0, -2260329440, 41244506419200]\) | \(311802066473807207098058600161/1033693082103011001480900\) | \(4234006864293933062065766400\) | \([2, 4]\) | \(301989888\) | \(4.1659\) | |
| 371280.cy3 | 371280cy4 | \([0, -1, 0, -2224245920, -40375167552768]\) | \(297106512928238351998640242081/3977028808593750000\) | \(16289910000000000000000\) | \([2]\) | \(150994944\) | \(3.8194\) | |
| 371280.cy4 | 371280cy8 | \([0, -1, 0, -1286483840, 77018919304320]\) | \(-57487943130312093140621093761/592356094985924086700006670\) | \(-2426290565062345059123227320320\) | \([4]\) | \(603979776\) | \(4.5125\) | |
| 371280.cy5 | 371280cy3 | \([0, -1, 0, -203937440, 16314489600]\) | \(229010110533436633465952161/132501160769452503210000\) | \(542724754511677453148160000\) | \([2, 4]\) | \(150994944\) | \(3.8194\) | |
| 371280.cy6 | 371280cy2 | \([0, -1, 0, -139137440, -629663750400]\) | \(72727020009972527154752161/265361167808100000000\) | \(1086919343341977600000000\) | \([2, 2]\) | \(75497472\) | \(3.4728\) | |
| 371280.cy7 | 371280cy1 | \([0, -1, 0, -4768160, -18767255808]\) | \(-2926956820564562516641/35459588343029760000\) | \(-145242473853049896960000\) | \([2]\) | \(37748736\) | \(3.1262\) | \(\Gamma_0(N)\)-optimal |
| 371280.cy8 | 371280cy6 | \([0, -1, 0, 815654560, 129693120000]\) | \(14651516183052242700771495839/8480668142378708755560900\) | \(-34736816711183191062777446400\) | \([4]\) | \(301989888\) | \(4.1659\) |
Rank
sage: E.rank()
The elliptic curves in class 371280.cy have rank \(0\).
Complex multiplication
The elliptic curves in class 371280.cy do not have complex multiplication.Modular form 371280.2.a.cy
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 16 & 4 & 4 & 8 & 16 & 8 \\ 2 & 1 & 8 & 2 & 2 & 4 & 8 & 4 \\ 16 & 8 & 1 & 16 & 4 & 2 & 4 & 8 \\ 4 & 2 & 16 & 1 & 4 & 8 & 16 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 2 & 8 & 2 & 1 & 2 & 4 \\ 16 & 8 & 4 & 16 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
