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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 51520b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51520.x1 | 51520b1 | \([0, 0, 0, -188, 912]\) | \(44851536/4025\) | \(65945600\) | \([2]\) | \(10240\) | \(0.24007\) | \(\Gamma_0(N)\)-optimal |
51520.x2 | 51520b2 | \([0, 0, 0, 212, 4272]\) | \(16078716/129605\) | \(-8493793280\) | \([2]\) | \(20480\) | \(0.58664\) |
Rank
sage: E.rank()
The elliptic curves in class 51520b have rank \(1\).
Complex multiplication
The elliptic curves in class 51520b do not have complex multiplication.Modular form 51520.2.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.