Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1452.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1452.c1 | 1452c2 | \([0, -1, 0, -156372, -23747832]\) | \(932410994128/29403\) | \(13334837269248\) | \([2]\) | \(7200\) | \(1.6143\) | |
1452.c2 | 1452c1 | \([0, -1, 0, -9357, -401850]\) | \(-3196715008/649539\) | \(-18411167366064\) | \([2]\) | \(3600\) | \(1.2677\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1452.c have rank \(1\).
Complex multiplication
The elliptic curves in class 1452.c do not have complex multiplication.Modular form 1452.2.a.c
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.