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SageMath
sage: E = EllipticCurve("s1")
sage: E.isogeny_class()
Elliptic curves in class 97461.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97461.s1 | 97461l6 | \([1, -1, 0, -17895348, -29112590781]\) | \(7389727131216686257/6115533215337\) | \(524505561726112197777\) | \([2]\) | \(4718592\) | \(2.9041\) | |
| 97461.s2 | 97461l4 | \([1, -1, 0, -1364463, -239747040]\) | \(3275619238041697/1605271262049\) | \(137677889298717241929\) | \([2, 2]\) | \(2359296\) | \(2.5576\) | |
| 97461.s3 | 97461l2 | \([1, -1, 0, -727218, 236274975]\) | \(495909170514577/6224736609\) | \(533871513200623689\) | \([2, 2]\) | \(1179648\) | \(2.2110\) | |
| 97461.s4 | 97461l1 | \([1, -1, 0, -725013, 237792456]\) | \(491411892194497/78897\) | \(6766689648537\) | \([2]\) | \(589824\) | \(1.8644\) | \(\Gamma_0(N)\)-optimal |
| 97461.s5 | 97461l3 | \([1, -1, 0, -125253, 615151746]\) | \(-2533811507137/1904381781393\) | \(-163331438293147586553\) | \([2]\) | \(2359296\) | \(2.5576\) | |
| 97461.s6 | 97461l5 | \([1, -1, 0, 4970502, -1839959199]\) | \(158346567380527343/108665074944153\) | \(-9319781966134294440513\) | \([2]\) | \(4718592\) | \(2.9041\) |
Rank
sage: E.rank()
The elliptic curves in class 97461.s have rank \(0\).
Complex multiplication
The elliptic curves in class 97461.s do not have complex multiplication.Modular form 97461.2.a.s
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
