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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 67760ca
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67760.q1 | 67760ca1 | \([0, -1, 0, -271080, -157187600]\) | \(-2509090441/10718750\) | \(-9411212311424000000\) | \([]\) | \(1368576\) | \(2.3258\) | \(\Gamma_0(N)\)-optimal |
67760.q2 | 67760ca2 | \([0, -1, 0, 2390920, 3791090800]\) | \(1721540467559/8070721400\) | \(-7086206190251021926400\) | \([]\) | \(4105728\) | \(2.8751\) |
Rank
sage: E.rank()
The elliptic curves in class 67760ca have rank \(0\).
Complex multiplication
The elliptic curves in class 67760ca do not have complex multiplication.Modular form 67760.2.a.ca
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.