Show commands:
SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 390775.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 390775.bc1 | 390775bc1 | \([0, 1, 1, -77583, -12559256]\) | \(-28094464000/20657483\) | \(-37973940897921875\) | \([]\) | \(2322432\) | \(1.8807\) | \(\Gamma_0(N)\)-optimal |
| 390775.bc2 | 390775bc2 | \([0, 1, 1, 632917, 193663369]\) | \(15252992000000/17621717267\) | \(-32393397105395046875\) | \([]\) | \(6967296\) | \(2.4301\) |
Rank
sage: E.rank()
The elliptic curves in class 390775.bc have rank \(1\).
Complex multiplication
The elliptic curves in class 390775.bc do not have complex multiplication.Modular form 390775.2.a.bc
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
