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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 1008m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1008.a2 | 1008m1 | \([0, 0, 0, -12, -65]\) | \(-16384/147\) | \(-1714608\) | \([2]\) | \(192\) | \(-0.12125\) | \(\Gamma_0(N)\)-optimal |
1008.a1 | 1008m2 | \([0, 0, 0, -327, -2270]\) | \(20720464/63\) | \(11757312\) | \([2]\) | \(384\) | \(0.22532\) |
Rank
sage: E.rank()
The elliptic curves in class 1008m have rank \(0\).
Complex multiplication
The elliptic curves in class 1008m do not have complex multiplication.Modular form 1008.2.a.m
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.