Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 6936h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6936.b3 | 6936h1 | \([0, -1, 0, -15124, 719428]\) | \(61918288/153\) | \(945420302592\) | \([4]\) | \(18432\) | \(1.1758\) | \(\Gamma_0(N)\)-optimal |
| 6936.b2 | 6936h2 | \([0, -1, 0, -20904, 125244]\) | \(40873252/23409\) | \(578597225186304\) | \([2, 2]\) | \(36864\) | \(1.5223\) | |
| 6936.b1 | 6936h3 | \([0, -1, 0, -217424, -38785716]\) | \(22994537186/111537\) | \(5513691204716544\) | \([2]\) | \(73728\) | \(1.8689\) | |
| 6936.b4 | 6936h4 | \([0, -1, 0, 83136, 915948]\) | \(1285471294/751689\) | \(-37158799573075968\) | \([2]\) | \(73728\) | \(1.8689\) |
Rank
sage: E.rank()
The elliptic curves in class 6936h have rank \(0\).
Complex multiplication
The elliptic curves in class 6936h do not have complex multiplication.Modular form 6936.2.a.h
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
