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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 15680cl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15680.ba2 | 15680cl1 | \([0, -1, 0, -261, 1891]\) | \(-262144/35\) | \(-263533760\) | \([]\) | \(4608\) | \(0.34838\) | \(\Gamma_0(N)\)-optimal |
| 15680.ba3 | 15680cl2 | \([0, -1, 0, 1699, -5165]\) | \(71991296/42875\) | \(-322828856000\) | \([]\) | \(13824\) | \(0.89769\) | |
| 15680.ba1 | 15680cl3 | \([0, -1, 0, -25741, -1654309]\) | \(-250523582464/13671875\) | \(-102942875000000\) | \([]\) | \(41472\) | \(1.4470\) |
Rank
sage: E.rank()
The elliptic curves in class 15680cl have rank \(1\).
Complex multiplication
The elliptic curves in class 15680cl do not have complex multiplication.Modular form 15680.2.a.cl
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.
