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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 435344.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435344.v1 | 435344v1 | \([0, -1, 0, -118130549, -494147779139]\) | \(-9221261135586623488/121324931\) | \(-2398667853312733184\) | \([]\) | \(41803776\) | \(3.0852\) | \(\Gamma_0(N)\)-optimal* |
435344.v2 | 435344v2 | \([0, -1, 0, -111451669, -552492436003]\) | \(-7743965038771437568/2189290237869371\) | \(-43283602734121045062201344\) | \([]\) | \(125411328\) | \(3.6345\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 435344.v have rank \(0\).
Complex multiplication
The elliptic curves in class 435344.v do not have complex multiplication.Modular form 435344.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.