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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 3381.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3381.g1 | 3381a1 | \([0, -1, 1, -303, -1933]\) | \(-62992384000/14283\) | \(-699867\) | \([]\) | \(768\) | \(0.11367\) | \(\Gamma_0(N)\)-optimal |
| 3381.g2 | 3381a2 | \([0, -1, 1, 117, -7120]\) | \(3584000000/444107667\) | \(-21761275683\) | \([]\) | \(2304\) | \(0.66298\) |
Rank
sage: E.rank()
The elliptic curves in class 3381.g have rank \(0\).
Complex multiplication
The elliptic curves in class 3381.g do not have complex multiplication.Modular form 3381.2.a.g
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.
