Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 428400.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
428400.c1 | 428400c2 | \([0, 0, 0, -4132875, -19133383750]\) | \(-6693187811305/131714173248\) | \(-153631411676467200000000\) | \([]\) | \(37324800\) | \(3.1300\) | |
428400.c2 | 428400c1 | \([0, 0, 0, 457125, 690826250]\) | \(9056932295/181997172\) | \(-212281501420800000000\) | \([]\) | \(12441600\) | \(2.5807\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 428400.c have rank \(0\).
Complex multiplication
The elliptic curves in class 428400.c do not have complex multiplication.Modular form 428400.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.