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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 34914.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
34914.v1 | 34914u2 | \([1, 1, 1, -104753, 6506015]\) | \(858729462625/371764272\) | \(55034454503957808\) | \([2]\) | \(405504\) | \(1.9084\) | |
34914.v2 | 34914u1 | \([1, 1, 1, 22207, 767423]\) | \(8181353375/6412032\) | \(-949210857416448\) | \([2]\) | \(202752\) | \(1.5619\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 34914.v have rank \(0\).
Complex multiplication
The elliptic curves in class 34914.v do not have complex multiplication.Modular form 34914.2.a.v
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.