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SageMath
E = EllipticCurve("gt1")
E.isogeny_class()
Elliptic curves in class 206400gt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
206400.he2 | 206400gt1 | \([0, 1, 0, 254367, 110404863]\) | \(444369620591/1540767744\) | \(-6310984679424000000\) | \([]\) | \(4515840\) | \(2.2904\) | \(\Gamma_0(N)\)-optimal |
206400.he1 | 206400gt2 | \([0, 1, 0, -95841633, -361217947137]\) | \(-23769846831649063249/3261823333284\) | \(-13360428373131264000000\) | \([]\) | \(31610880\) | \(3.2634\) |
Rank
sage: E.rank()
The elliptic curves in class 206400gt have rank \(1\).
Complex multiplication
The elliptic curves in class 206400gt do not have complex multiplication.Modular form 206400.2.a.gt
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.