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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 64400.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 64400.be1 | 64400g4 | \([0, 0, 0, -86075, -9719750]\) | \(4407931365156/100625\) | \(1610000000000\) | \([2]\) | \(122880\) | \(1.4558\) | |
| 64400.be2 | 64400g3 | \([0, 0, 0, -23075, 1207250]\) | \(84923690436/9794435\) | \(156710960000000\) | \([4]\) | \(122880\) | \(1.4558\) | |
| 64400.be3 | 64400g2 | \([0, 0, 0, -5575, -140250]\) | \(4790692944/648025\) | \(2592100000000\) | \([2, 2]\) | \(61440\) | \(1.1092\) | |
| 64400.be4 | 64400g1 | \([0, 0, 0, 550, -11625]\) | \(73598976/276115\) | \(-69028750000\) | \([2]\) | \(30720\) | \(0.76264\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 64400.be have rank \(0\).
Complex multiplication
The elliptic curves in class 64400.be do not have complex multiplication.Modular form 64400.2.a.be
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
