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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 5712s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5712.p2 | 5712s1 | \([0, 1, 0, -344, -3564]\) | \(-1102302937/616896\) | \(-2526806016\) | \([2]\) | \(2304\) | \(0.50748\) | \(\Gamma_0(N)\)-optimal |
| 5712.p1 | 5712s2 | \([0, 1, 0, -6104, -185580]\) | \(6141556990297/1019592\) | \(4176248832\) | \([2]\) | \(4608\) | \(0.85405\) |
Rank
sage: E.rank()
The elliptic curves in class 5712s have rank \(0\).
Complex multiplication
The elliptic curves in class 5712s do not have complex multiplication.Modular form 5712.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
