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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 4788.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4788.a1 | 4788d2 | \([0, 0, 0, -1658271, 238995430]\) | \(2702232642991073488/1431572558302971\) | \(267165797120733659904\) | \([2]\) | \(135168\) | \(2.6110\) | |
| 4788.a2 | 4788d1 | \([0, 0, 0, 394584, 29193649]\) | \(582498235727347712/368659410191667\) | \(-4300043360475603888\) | \([2]\) | \(67584\) | \(2.2644\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4788.a have rank \(0\).
Complex multiplication
The elliptic curves in class 4788.a do not have complex multiplication.Modular form 4788.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
