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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 38025cg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38025.bu2 | 38025cg1 | \([0, 0, 1, -126750, -16134219]\) | \(163840/13\) | \(17868620661328125\) | \([]\) | \(302400\) | \(1.8621\) | \(\Gamma_0(N)\)-optimal |
38025.bu1 | 38025cg2 | \([0, 0, 1, -2028000, 1108455156]\) | \(671088640/2197\) | \(3019796891764453125\) | \([]\) | \(907200\) | \(2.4114\) |
Rank
sage: E.rank()
The elliptic curves in class 38025cg have rank \(1\).
Complex multiplication
The elliptic curves in class 38025cg do not have complex multiplication.Modular form 38025.2.a.cg
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.