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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 7350.cf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7350.cf1 | 7350bx1 | \([1, 1, 1, -1308938, 328171031]\) | \(393349474783/153600000\) | \(96848656800000000000\) | \([2]\) | \(376320\) | \(2.5337\) | \(\Gamma_0(N)\)-optimal |
7350.cf2 | 7350bx2 | \([1, 1, 1, 4179062, 2369707031]\) | \(12801408679457/11250000000\) | \(-7093407480468750000000\) | \([2]\) | \(752640\) | \(2.8803\) |
Rank
sage: E.rank()
The elliptic curves in class 7350.cf have rank \(1\).
Complex multiplication
The elliptic curves in class 7350.cf do not have complex multiplication.Modular form 7350.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.