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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 91035.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91035.ba1 | 91035d3 | \([0, 0, 1, -341598, 80387734]\) | \(-250523582464/13671875\) | \(-240574247279296875\) | \([]\) | \(907200\) | \(2.0934\) | |
| 91035.ba2 | 91035d1 | \([0, 0, 1, -3468, -87206]\) | \(-262144/35\) | \(-615870073035\) | \([]\) | \(100800\) | \(0.99476\) | \(\Gamma_0(N)\)-optimal |
| 91035.ba3 | 91035d2 | \([0, 0, 1, 22542, 222313]\) | \(71991296/42875\) | \(-754440839467875\) | \([]\) | \(302400\) | \(1.5441\) |
Rank
sage: E.rank()
The elliptic curves in class 91035.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 91035.ba do not have complex multiplication.Modular form 91035.2.a.ba
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 LMFDB numbering.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
