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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 91035.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91035.g1 | 91035n4 | \([1, -1, 1, -8293343, 9194060972]\) | \(3585019225176649/316207395\) | \(5564076327224488395\) | \([2]\) | \(3538944\) | \(2.6377\) | |
| 91035.g2 | 91035n3 | \([1, -1, 1, -3013313, -1910169844]\) | \(171963096231529/9865918125\) | \(173603534748602293125\) | \([2]\) | \(3538944\) | \(2.6377\) | |
| 91035.g3 | 91035n2 | \([1, -1, 1, -555368, 122059082]\) | \(1076575468249/258084225\) | \(4541324299998039225\) | \([2, 2]\) | \(1769472\) | \(2.2912\) | |
| 91035.g4 | 91035n1 | \([1, -1, 1, 81877, 11943146]\) | \(3449795831/5510295\) | \(-96960736688411295\) | \([2]\) | \(884736\) | \(1.9446\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 91035.g have rank \(0\).
Complex multiplication
The elliptic curves in class 91035.g do not have complex multiplication.Modular form 91035.2.a.g
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.
