Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 348480.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 348480.l1 | 348480l2 | \([0, 0, 0, -6372828, 6192088848]\) | \(1016339184/25\) | \(704079407816294400\) | \([2]\) | \(12976128\) | \(2.5341\) | |
| 348480.l2 | 348480l1 | \([0, 0, 0, -383328, 104361048]\) | \(-3538944/625\) | \(-1100124074712960000\) | \([2]\) | \(6488064\) | \(2.1875\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 348480.l have rank \(1\).
Complex multiplication
The elliptic curves in class 348480.l do not have complex multiplication.Modular form 348480.2.a.l
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.
