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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 310464.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
310464.b1 | 310464b2 | \([0, 0, 0, -52332, 4582480]\) | \(19034163/121\) | \(100757479882752\) | \([2]\) | \(1474560\) | \(1.5240\) | |
310464.b2 | 310464b1 | \([0, 0, 0, -5292, -27440]\) | \(19683/11\) | \(9159770898432\) | \([2]\) | \(737280\) | \(1.1774\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 310464.b have rank \(1\).
Complex multiplication
The elliptic curves in class 310464.b do not have complex multiplication.Modular form 310464.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.