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SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 349830.du
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 349830.du1 | 349830du2 | \([1, -1, 1, -1195538, 348768281]\) | \(53706380371489/16171875000\) | \(56904684259921875000\) | \([2]\) | \(9031680\) | \(2.4959\) | |
| 349830.du2 | 349830du1 | \([1, -1, 1, 203782, 36440057]\) | \(265971760991/317400000\) | \(-1116849269741400000\) | \([2]\) | \(4515840\) | \(2.1493\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 349830.du have rank \(1\).
Complex multiplication
The elliptic curves in class 349830.du do not have complex multiplication.Modular form 349830.2.a.du
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.
