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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 3015c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3015.c2 | 3015c1 | \([0, 0, 1, 2148, -5823]\) | \(1503484706816/890163675\) | \(-648929319075\) | \([]\) | \(3840\) | \(0.95590\) | \(\Gamma_0(N)\)-optimal |
3015.c1 | 3015c2 | \([0, 0, 1, -27012, 1887390]\) | \(-2989967081734144/380653171875\) | \(-277496162296875\) | \([3]\) | \(11520\) | \(1.5052\) |
Rank
sage: E.rank()
The elliptic curves in class 3015c have rank \(0\).
Complex multiplication
The elliptic curves in class 3015c do not have complex multiplication.Modular form 3015.2.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 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.