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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 435344.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435344.c1 | 435344c2 | \([0, 1, 0, -21161560, 37460475924]\) | \(53008645999484449/2060047808\) | \(40728401101146816512\) | \([2]\) | \(40255488\) | \(2.8473\) | \(\Gamma_0(N)\)-optimal* |
435344.c2 | 435344c1 | \([0, 1, 0, -1260120, 642811924]\) | \(-11192824869409/2563305472\) | \(-50678111936507281408\) | \([2]\) | \(20127744\) | \(2.5007\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 435344.c have rank \(0\).
Complex multiplication
The elliptic curves in class 435344.c do not have complex multiplication.Modular form 435344.2.a.c
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.