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SageMath
E = EllipticCurve("gt1")
E.isogeny_class()
Elliptic curves in class 62400.gt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
62400.gt1 | 62400gk2 | \([0, 1, 0, -73633, 6864863]\) | \(10779215329/1232010\) | \(5046312960000000\) | \([2]\) | \(442368\) | \(1.7454\) | |
62400.gt2 | 62400gk1 | \([0, 1, 0, 6367, 544863]\) | \(6967871/35100\) | \(-143769600000000\) | \([2]\) | \(221184\) | \(1.3988\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 62400.gt have rank \(1\).
Complex multiplication
The elliptic curves in class 62400.gt do not have complex multiplication.Modular form 62400.2.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 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.