Show commands:
SageMath
E = EllipticCurve("fe1")
E.isogeny_class()
Elliptic curves in class 57330.fe
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57330.fe1 | 57330et1 | \([1, -1, 1, -3317, -93859]\) | \(-2305248169/878800\) | \(-1538189125200\) | \([]\) | \(124416\) | \(1.0481\) | \(\Gamma_0(N)\)-optimal |
| 57330.fe2 | 57330et2 | \([1, -1, 1, 25348, 972479]\) | \(1029084842471/832000000\) | \(-1456273728000000\) | \([3]\) | \(373248\) | \(1.5974\) |
Rank
sage: E.rank()
The elliptic curves in class 57330.fe have rank \(1\).
Complex multiplication
The elliptic curves in class 57330.fe do not have complex multiplication.Modular form 57330.2.a.fe
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.
