Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 443822.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
443822.g1 | 443822g2 | \([1, 0, 1, -65674479, -204852654030]\) | \(1413378216646643521/49232902384\) | \(1091215827867781031536\) | \([]\) | \(36192000\) | \(3.1273\) | |
443822.g2 | 443822g1 | \([1, 0, 1, -1179839, 488841490]\) | \(8194759433281/82837504\) | \(1836040353680982016\) | \([]\) | \(7238400\) | \(2.3225\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 443822.g have rank \(0\).
Complex multiplication
The elliptic curves in class 443822.g do not have complex multiplication.Modular form 443822.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.