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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 301530.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
301530.c1 | 301530c2 | \([1, 1, 0, -443954003, -3594611905347]\) | \(65368817122122518102281/126164412052023600\) | \(18676860898283627874980400\) | \([2]\) | \(118947840\) | \(3.7381\) | |
301530.c2 | 301530c1 | \([1, 1, 0, -18595683, -93827860083]\) | \(-4803890892670577161/22906688895164160\) | \(-3391012054642054226538240\) | \([2]\) | \(59473920\) | \(3.3915\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 301530.c have rank \(0\).
Complex multiplication
The elliptic curves in class 301530.c do not have complex multiplication.Modular form 301530.2.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.