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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 13005g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13005.g2 | 13005g1 | \([0, 0, 1, -11525898, -919712372]\) | \(115220905984/66430125\) | \(97629667841621112445125\) | \([]\) | \(940032\) | \(3.1008\) | \(\Gamma_0(N)\)-optimal |
| 13005.g1 | 13005g2 | \([0, 0, 1, -620393988, 5947660640119]\) | \(17968412610002944/158203125\) | \(232504734038306642578125\) | \([]\) | \(2820096\) | \(3.6501\) |
Rank
sage: E.rank()
The elliptic curves in class 13005g have rank \(0\).
Complex multiplication
The elliptic curves in class 13005g do not have complex multiplication.Modular form 13005.2.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 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.
