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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 290445c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 290445.c2 | 290445c1 | \([0, -1, 1, 68975, 1036533]\) | \(1503484706816/890163675\) | \(-21486387126606075\) | \([]\) | \(2419200\) | \(1.8232\) | \(\Gamma_0(N)\)-optimal |
| 290445.c1 | 290445c2 | \([0, -1, 1, -867385, -343145994]\) | \(-2989967081734144/380653171875\) | \(-9188042201201671875\) | \([]\) | \(7257600\) | \(2.3725\) |
Rank
sage: E.rank()
The elliptic curves in class 290445c have rank \(1\).
Complex multiplication
The elliptic curves in class 290445c do not have complex multiplication.Modular form 290445.2.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.
