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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 5808a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5808.e1 | 5808a1 | \([0, -1, 0, -84, 288]\) | \(194672/27\) | \(9199872\) | \([2]\) | \(1152\) | \(0.062749\) | \(\Gamma_0(N)\)-optimal |
5808.e2 | 5808a2 | \([0, -1, 0, 136, 1344]\) | \(202612/729\) | \(-993586176\) | \([2]\) | \(2304\) | \(0.40932\) |
Rank
sage: E.rank()
The elliptic curves in class 5808a have rank \(1\).
Complex multiplication
The elliptic curves in class 5808a do not have complex multiplication.Modular form 5808.2.a.a
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.