Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 19950.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19950.c1 | 19950n2 | \([1, 1, 0, -933200, 362784000]\) | \(-46017030564782549/2542728609792\) | \(-4966266816000000000\) | \([]\) | \(600000\) | \(2.3453\) | |
19950.c2 | 19950n1 | \([1, 1, 0, 4925, -1362875]\) | \(6761990971/415984632\) | \(-812469984375000\) | \([]\) | \(120000\) | \(1.5405\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19950.c have rank \(0\).
Complex multiplication
The elliptic curves in class 19950.c do not have complex multiplication.Modular form 19950.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.