Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 1224.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1224.d1 | 1224d2 | \([0, 0, 0, -435, -3346]\) | \(6097250/289\) | \(431474688\) | \([2]\) | \(384\) | \(0.41746\) | |
| 1224.d2 | 1224d1 | \([0, 0, 0, -75, 182]\) | \(62500/17\) | \(12690432\) | \([2]\) | \(192\) | \(0.070888\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1224.d have rank \(1\).
Complex multiplication
The elliptic curves in class 1224.d do not have complex multiplication.Modular form 1224.2.a.d
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.
