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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 37752s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37752.g1 | 37752s1 | \([0, -1, 0, -403, 1564]\) | \(256000/117\) | \(3316362192\) | \([2]\) | \(22400\) | \(0.52177\) | \(\Gamma_0(N)\)-optimal |
| 37752.g2 | 37752s2 | \([0, -1, 0, 1412, 10276]\) | \(686000/507\) | \(-229934445312\) | \([2]\) | \(44800\) | \(0.86835\) |
Rank
sage: E.rank()
The elliptic curves in class 37752s have rank \(0\).
Complex multiplication
The elliptic curves in class 37752s do not have complex multiplication.Modular form 37752.2.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.
