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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 36414.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 36414.x1 | 36414be2 | \([1, -1, 0, -72882, -890838]\) | \(2433138625/1387778\) | \(24419741091896178\) | \([2]\) | \(221184\) | \(1.8343\) | |
| 36414.x2 | 36414be1 | \([1, -1, 0, -46872, 3900204]\) | \(647214625/3332\) | \(58630830952932\) | \([2]\) | \(110592\) | \(1.4877\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 36414.x have rank \(1\).
Complex multiplication
The elliptic curves in class 36414.x do not have complex multiplication.Modular form 36414.2.a.x
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.
