Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 43681.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43681.c1 | 43681l2 | \([1, 0, 0, -1311340, -578120487]\) | \(-24729001\) | \(-10084702406819161\) | \([]\) | \(432432\) | \(2.1532\) | |
43681.c2 | 43681l1 | \([1, 0, 0, -910, 41229]\) | \(-121\) | \(-688798743721\) | \([]\) | \(39312\) | \(0.95426\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 43681.c have rank \(1\).
Complex multiplication
The elliptic curves in class 43681.c do not have complex multiplication.Modular form 43681.2.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.
\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.