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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 86640.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 86640.ba1 | 86640cs4 | \([0, -1, 0, -2844564600, 58395430849392]\) | \(13209596798923694545921/92340\) | \(17793911404707840\) | \([4]\) | \(33177600\) | \(3.6529\) | |
| 86640.ba2 | 86640cs3 | \([0, -1, 0, -179980280, 888788204400]\) | \(3345930611358906241/165622259047500\) | \(31915397489049019791360000\) | \([2]\) | \(33177600\) | \(3.6529\) | |
| 86640.ba3 | 86640cs2 | \([0, -1, 0, -177785400, 912471837552]\) | \(3225005357698077121/8526675600\) | \(1643089779110721945600\) | \([2, 2]\) | \(16588800\) | \(3.3063\) | |
| 86640.ba4 | 86640cs1 | \([0, -1, 0, -10974520, 14628957040]\) | \(-758575480593601/40535043840\) | \(-7811100052793028771840\) | \([2]\) | \(8294400\) | \(2.9597\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 86640.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 86640.ba do not have complex multiplication.Modular form 86640.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
