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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 61370.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
61370.c1 | 61370d2 | \([1, 1, 0, -2397408, 1473834112]\) | \(-32391289681150609/1228250000000\) | \(-57784103338250000000\) | \([]\) | \(1809864\) | \(2.5620\) | |
61370.c2 | 61370d1 | \([1, 1, 0, 144032, 6591488]\) | \(7023836099951/4456448000\) | \(-209657522290688000\) | \([]\) | \(603288\) | \(2.0127\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 61370.c have rank \(0\).
Complex multiplication
The elliptic curves in class 61370.c do not have complex multiplication.Modular form 61370.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.