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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 113850.cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
113850.cc1 | 113850l1 | \([1, -1, 0, -867, 18541]\) | \(-170953875/244904\) | \(-103318875000\) | \([]\) | \(124416\) | \(0.80554\) | \(\Gamma_0(N)\)-optimal |
113850.cc2 | 113850l2 | \([1, -1, 0, 7383, -363709]\) | \(144703125/267674\) | \(-82322302218750\) | \([]\) | \(373248\) | \(1.3548\) |
Rank
sage: E.rank()
The elliptic curves in class 113850.cc have rank \(1\).
Complex multiplication
The elliptic curves in class 113850.cc do not have complex multiplication.Modular form 113850.2.a.cc
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.