Show commands:
SageMath
E = EllipticCurve("gi1")
E.isogeny_class()
Elliptic curves in class 270400gi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270400.gi2 | 270400gi1 | \([0, 1, 0, -2253, 37493]\) | \(163840/13\) | \(100397627200\) | \([]\) | \(290304\) | \(0.85462\) | \(\Gamma_0(N)\)-optimal |
| 270400.gi1 | 270400gi2 | \([0, 1, 0, -36053, -2639467]\) | \(671088640/2197\) | \(16967198996800\) | \([]\) | \(870912\) | \(1.4039\) |
Rank
sage: E.rank()
The elliptic curves in class 270400gi have rank \(1\).
Complex multiplication
The elliptic curves in class 270400gi do not have complex multiplication.Modular form 270400.2.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 Cremona 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 Cremona labels.
