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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 372645ci
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
372645.ci2 | 372645ci1 | \([0, 0, 1, 99372, 15636598]\) | \(7077888/10985\) | \(-168427180809100395\) | \([]\) | \(3048192\) | \(1.9907\) | \(\Gamma_0(N)\)-optimal |
372645.ci1 | 372645ci2 | \([0, 0, 1, -3130218, 2141460389]\) | \(-303464448/1625\) | \(-18163227042874879875\) | \([]\) | \(9144576\) | \(2.5400\) |
Rank
sage: E.rank()
The elliptic curves in class 372645ci have rank \(0\).
Complex multiplication
The elliptic curves in class 372645ci do not have complex multiplication.Modular form 372645.2.a.ci
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 Cremona 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 Cremona labels.