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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 54390.cv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54390.cv1 | 54390cv4 | \([1, 0, 0, -16709246, -26290956924]\) | \(4385367890843575421521/24975000000\) | \(2938283775000000\) | \([2]\) | \(2654208\) | \(2.5798\) | |
| 54390.cv2 | 54390cv6 | \([1, 0, 0, -14853126, 21936037500]\) | \(3080272010107543650001/15465841417699560\) | \(1819540776950935534440\) | \([2]\) | \(5308416\) | \(2.9263\) | |
| 54390.cv3 | 54390cv3 | \([1, 0, 0, -1436926, -74580220]\) | \(2788936974993502801/1593609593601600\) | \(187486575077634638400\) | \([2, 2]\) | \(2654208\) | \(2.5798\) | |
| 54390.cv4 | 54390cv2 | \([1, 0, 0, -1044926, -410367420]\) | \(1072487167529950801/2554882560000\) | \(300579378301440000\) | \([2, 2]\) | \(1327104\) | \(2.2332\) | |
| 54390.cv5 | 54390cv1 | \([1, 0, 0, -41406, -11167164]\) | \(-66730743078481/419010969600\) | \(-49296221562470400\) | \([2]\) | \(663552\) | \(1.8866\) | \(\Gamma_0(N)\)-optimal |
| 54390.cv6 | 54390cv5 | \([1, 0, 0, 5707274, -593249140]\) | \(174751791402194852399/102423900876336360\) | \(-12050069514200096417640\) | \([2]\) | \(5308416\) | \(2.9263\) |
Rank
sage: E.rank()
The elliptic curves in class 54390.cv have rank \(1\).
Complex multiplication
The elliptic curves in class 54390.cv do not have complex multiplication.Modular form 54390.2.a.cv
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
