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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 215950.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
215950.b1 | 215950s2 | \([1, 1, 0, -18000, -21620000]\) | \(-41281826100481/12890495001440\) | \(-201413984397500000\) | \([]\) | \(1823040\) | \(1.9995\) | |
215950.b2 | 215950s1 | \([1, 1, 0, 2000, 800000]\) | \(56578878719/17690624000\) | \(-276416000000000\) | \([]\) | \(607680\) | \(1.4502\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 215950.b have rank \(0\).
Complex multiplication
The elliptic curves in class 215950.b do not have complex multiplication.Modular form 215950.2.a.b
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.