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SageMath
E = EllipticCurve("gi1")
E.isogeny_class()
Elliptic curves in class 338800.gi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 338800.gi1 | 338800gi1 | \([0, 1, 0, -20619408, 36105831188]\) | \(-584043889/1400\) | \(-2323993244249600000000\) | \([]\) | \(21897216\) | \(2.9792\) | \(\Gamma_0(N)\)-optimal |
| 338800.gi2 | 338800gi2 | \([0, 1, 0, 37944592, 181930191188]\) | \(3639707951/10718750\) | \(-17793073276286000000000000\) | \([]\) | \(65691648\) | \(3.5285\) |
Rank
sage: E.rank()
The elliptic curves in class 338800.gi have rank \(1\).
Complex multiplication
The elliptic curves in class 338800.gi do not have complex multiplication.Modular form 338800.2.a.gi
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
