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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 14784.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14784.m1 | 14784f2 | \([0, -1, 0, -28943073, 59091007329]\) | \(10228636028672744397625/167006381634183168\) | \(43779720907111312392192\) | \([2]\) | \(1597440\) | \(3.1437\) | |
14784.m2 | 14784f1 | \([0, -1, 0, -107233, 2590062433]\) | \(-520203426765625/11054534935707648\) | \(-2897880006186145677312\) | \([2]\) | \(798720\) | \(2.7971\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14784.m have rank \(0\).
Complex multiplication
The elliptic curves in class 14784.m do not have complex multiplication.Modular form 14784.2.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 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.