Show commands:
SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 12480cl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12480.cc2 | 12480cl1 | \([0, 1, 0, -281, 2919]\) | \(-601211584/609375\) | \(-2496000000\) | \([2]\) | \(7680\) | \(0.49873\) | \(\Gamma_0(N)\)-optimal |
| 12480.cc1 | 12480cl2 | \([0, 1, 0, -5281, 145919]\) | \(497169541448/190125\) | \(6230016000\) | \([2]\) | \(15360\) | \(0.84530\) |
Rank
sage: E.rank()
The elliptic curves in class 12480cl have rank \(1\).
Complex multiplication
The elliptic curves in class 12480cl do not have complex multiplication.Modular form 12480.2.a.cl
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 Cremona 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 Cremona labels.
