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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 3249c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3249.d3 | 3249c1 | \([0, 0, 1, 2166, -1715]\) | \(32768/19\) | \(-651632497731\) | \([]\) | \(2880\) | \(0.95635\) | \(\Gamma_0(N)\)-optimal |
| 3249.d2 | 3249c2 | \([0, 0, 1, -30324, -2162300]\) | \(-89915392/6859\) | \(-235239331680891\) | \([]\) | \(8640\) | \(1.5057\) | |
| 3249.d1 | 3249c3 | \([0, 0, 1, -2499564, -1521053555]\) | \(-50357871050752/19\) | \(-651632497731\) | \([]\) | \(25920\) | \(2.0550\) |
Rank
sage: E.rank()
The elliptic curves in class 3249c have rank \(1\).
Complex multiplication
The elliptic curves in class 3249c do not have complex multiplication.Modular form 3249.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
