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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 59290.cf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59290.cf1 | 59290f1 | \([1, -1, 0, -780775, -265350079]\) | \(-5154200289/20\) | \(-204253932487220\) | \([]\) | \(1176000\) | \(1.9591\) | \(\Gamma_0(N)\)-optimal |
59290.cf2 | 59290f2 | \([1, -1, 0, 5444675, 2518173125]\) | \(1747829720511/1280000000\) | \(-13072251679182080000000\) | \([]\) | \(8232000\) | \(2.9320\) |
Rank
sage: E.rank()
The elliptic curves in class 59290.cf have rank \(0\).
Complex multiplication
The elliptic curves in class 59290.cf do not have complex multiplication.Modular form 59290.2.a.cf
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.