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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 271440c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
271440.c1 | 271440c1 | \([0, 0, 0, -5628, -162497]\) | \(1690201440256/152685\) | \(1780917840\) | \([2]\) | \(368640\) | \(0.81462\) | \(\Gamma_0(N)\)-optimal |
271440.c2 | 271440c2 | \([0, 0, 0, -5223, -186878]\) | \(-84433792336/31979025\) | \(-5968053561600\) | \([2]\) | \(737280\) | \(1.1612\) |
Rank
sage: E.rank()
The elliptic curves in class 271440c have rank \(1\).
Complex multiplication
The elliptic curves in class 271440c do not have complex multiplication.Modular form 271440.2.a.c
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.