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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 118580.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 118580.ba1 | 118580m4 | \([0, -1, 0, -42097876, -105118787640]\) | \(154639330142416/33275\) | \(1775425202550137600\) | \([2]\) | \(7464960\) | \(2.8864\) | |
| 118580.ba2 | 118580m3 | \([0, -1, 0, -2640381, -1629669754]\) | \(610462990336/8857805\) | \(29538636807427914320\) | \([2]\) | \(3732480\) | \(2.5398\) | |
| 118580.ba3 | 118580m2 | \([0, -1, 0, -594876, -99596440]\) | \(436334416/171875\) | \(9170584723916000000\) | \([2]\) | \(2488320\) | \(2.3370\) | |
| 118580.ba4 | 118580m1 | \([0, -1, 0, -268781, 52624706]\) | \(643956736/15125\) | \(50438215981538000\) | \([2]\) | \(1244160\) | \(1.9905\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 118580.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 118580.ba do not have complex multiplication.Modular form 118580.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
