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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 4788.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4788.b1 | 4788a2 | \([0, 0, 0, -114735, 14783078]\) | \(895043160898000/12086562663\) | \(2255642670419712\) | \([2]\) | \(21504\) | \(1.7526\) | |
| 4788.b2 | 4788a1 | \([0, 0, 0, -1020, 614189]\) | \(-10061824000/13965589323\) | \(-162894633863472\) | \([2]\) | \(10752\) | \(1.4060\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4788.b have rank \(1\).
Complex multiplication
The elliptic curves in class 4788.b do not have complex multiplication.Modular form 4788.2.a.b
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.
