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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 4788.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4788.c1 | 4788b2 | \([0, 0, 0, -13215, 410006]\) | \(1367595682000/402300927\) | \(75079008200448\) | \([2]\) | \(13824\) | \(1.3683\) | |
| 4788.c2 | 4788b1 | \([0, 0, 0, 2220, 42653]\) | \(103737344000/127413867\) | \(-1486155344688\) | \([2]\) | \(6912\) | \(1.0217\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4788.c have rank \(0\).
Complex multiplication
The elliptic curves in class 4788.c do not have complex multiplication.Modular form 4788.2.a.c
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.
