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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 13328.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13328.g1 | 13328y2 | \([0, 1, 0, -548816, 155990932]\) | \(37936442980801/88817792\) | \(42800432787488768\) | \([2]\) | \(258048\) | \(2.0715\) | |
| 13328.g2 | 13328y1 | \([0, 1, 0, -47056, 445332]\) | \(23912763841/13647872\) | \(6576777187033088\) | \([2]\) | \(129024\) | \(1.7250\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13328.g have rank \(0\).
Complex multiplication
The elliptic curves in class 13328.g do not have complex multiplication.Modular form 13328.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
