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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 5808b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5808.d1 | 5808b1 | \([0, -1, 0, -10204, -342560]\) | \(194672/27\) | \(16298134440192\) | \([2]\) | \(12672\) | \(1.2617\) | \(\Gamma_0(N)\)-optimal |
| 5808.d2 | 5808b2 | \([0, -1, 0, 16416, -1854576]\) | \(202612/729\) | \(-1760198519540736\) | \([2]\) | \(25344\) | \(1.6083\) |
Rank
sage: E.rank()
The elliptic curves in class 5808b have rank \(1\).
Complex multiplication
The elliptic curves in class 5808b do not have complex multiplication.Modular form 5808.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
