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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 26299c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26299.g2 | 26299c1 | \([0, -1, 1, -2119, 38327]\) | \(-43614208/91\) | \(-2196518779\) | \([]\) | \(18432\) | \(0.67810\) | \(\Gamma_0(N)\)-optimal |
| 26299.g3 | 26299c2 | \([0, -1, 1, 3661, 185428]\) | \(224755712/753571\) | \(-18189372008899\) | \([]\) | \(55296\) | \(1.2274\) | |
| 26299.g1 | 26299c3 | \([0, -1, 1, -33909, -5912183]\) | \(-178643795968/524596891\) | \(-12662493653697979\) | \([]\) | \(165888\) | \(1.7767\) |
Rank
sage: E.rank()
The elliptic curves in class 26299c have rank \(0\).
Complex multiplication
The elliptic curves in class 26299c do not have complex multiplication.Modular form 26299.2.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.
