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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 116380b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116380.j2 | 116380b1 | \([0, -1, 0, -2821, -2214]\) | \(1048576/605\) | \(1432987405520\) | \([2]\) | \(142560\) | \(1.0221\) | \(\Gamma_0(N)\)-optimal |
116380.j1 | 116380b2 | \([0, -1, 0, -31916, -2178520]\) | \(94875856/275\) | \(10421726585600\) | \([2]\) | \(285120\) | \(1.3687\) |
Rank
sage: E.rank()
The elliptic curves in class 116380b have rank \(1\).
Complex multiplication
The elliptic curves in class 116380b do not have complex multiplication.Modular form 116380.2.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 Cremona 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 Cremona labels.