Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 31824.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 31824.g1 | 31824v1 | \([0, 0, 0, -7851, -258086]\) | \(17923019113/735488\) | \(2196155400192\) | \([2]\) | \(36864\) | \(1.1337\) | \(\Gamma_0(N)\)-optimal |
| 31824.g2 | 31824v2 | \([0, 0, 0, 3669, -951590]\) | \(1829276567/132066064\) | \(-394347154046976\) | \([2]\) | \(73728\) | \(1.4802\) |
Rank
sage: E.rank()
The elliptic curves in class 31824.g have rank \(1\).
Complex multiplication
The elliptic curves in class 31824.g do not have complex multiplication.Modular form 31824.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
