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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 151725.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
151725.s1 | 151725bi2 | \([1, 1, 1, -4324313, -2825357344]\) | \(23711636464489/4590075735\) | \(1731144840137315859375\) | \([2]\) | \(7962624\) | \(2.7923\) | |
151725.s2 | 151725bi1 | \([1, 1, 1, 552562, -260121094]\) | \(49471280711/106269975\) | \(-40079669596730859375\) | \([2]\) | \(3981312\) | \(2.4457\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 151725.s have rank \(1\).
Complex multiplication
The elliptic curves in class 151725.s do not have complex multiplication.Modular form 151725.2.a.s
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.