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SageMath
E = EllipticCurve("em1")
E.isogeny_class()
Elliptic curves in class 310464.em
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
310464.em1 | 310464em2 | \([0, 0, 0, -14679756, 21648428144]\) | \(144106117295241933/247808\) | \(601607343439872\) | \([2]\) | \(7569408\) | \(2.5248\) | |
310464.em2 | 310464em1 | \([0, 0, 0, -917196, 338480240]\) | \(-35148950502093/46137344\) | \(-112008349033168896\) | \([2]\) | \(3784704\) | \(2.1782\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 310464.em have rank \(1\).
Complex multiplication
The elliptic curves in class 310464.em do not have complex multiplication.Modular form 310464.2.a.em
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.