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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 1006.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1006.a1 | 1006b2 | \([1, -1, 0, -32, 24]\) | \(3687953625/2024072\) | \(2024072\) | \([2]\) | \(126\) | \(-0.099277\) | |
1006.a2 | 1006b1 | \([1, -1, 0, 8, 0]\) | \(52734375/32192\) | \(-32192\) | \([2]\) | \(63\) | \(-0.44585\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1006.a have rank \(0\).
Complex multiplication
The elliptic curves in class 1006.a do not have complex multiplication.Modular form 1006.2.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 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.