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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 344760.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 344760.s1 | 344760s4 | \([0, -1, 0, -1678051080, -26457371559828]\) | \(52862679907533400952738/90903515625\) | \(898608962253600000000\) | \([2]\) | \(121110528\) | \(3.7095\) | |
| 344760.s2 | 344760s2 | \([0, -1, 0, -104911200, -413096962500]\) | \(25836234020391349156/33847087730625\) | \(167294389946337613440000\) | \([2, 2]\) | \(60555264\) | \(3.3629\) | |
| 344760.s3 | 344760s3 | \([0, -1, 0, -76350200, -643035861300]\) | \(-4979252943420552578/15190164405108225\) | \(-150159405592690742075443200\) | \([2]\) | \(121110528\) | \(3.7095\) | |
| 344760.s4 | 344760s1 | \([0, -1, 0, -8375020, -2586510668]\) | \(52575237512036944/28081530070425\) | \(34699310611890694099200\) | \([2]\) | \(30277632\) | \(3.0164\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 344760.s have rank \(1\).
Complex multiplication
The elliptic curves in class 344760.s do not have complex multiplication.Modular form 344760.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
