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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 91035.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91035.p1 | 91035w4 | \([1, -1, 1, -57816383, 169223588682]\) | \(1214661886599131209/2213451765\) | \(38948534290571418765\) | \([2]\) | \(7077888\) | \(3.0161\) | |
| 91035.p2 | 91035w3 | \([1, -1, 1, -9619853, -8030337294]\) | \(5595100866606889/1653777286875\) | \(29100341098609439911875\) | \([2]\) | \(7077888\) | \(3.0161\) | |
| 91035.p3 | 91035w2 | \([1, -1, 1, -3650558, 2587844652]\) | \(305759741604409/12646127025\) | \(222524890699903922025\) | \([2, 2]\) | \(3538944\) | \(2.6695\) | |
| 91035.p4 | 91035w1 | \([1, -1, 1, 107887, 149365536]\) | \(7892485271/552491415\) | \(-9721797945921728415\) | \([2]\) | \(1769472\) | \(2.3230\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 91035.p have rank \(1\).
Complex multiplication
The elliptic curves in class 91035.p do not have complex multiplication.Modular form 91035.2.a.p
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
