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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 6400.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6400.t1 | 6400b1 | \([0, 1, 0, -63, 173]\) | \(-2194880\) | \(-12800\) | \([]\) | \(576\) | \(-0.25459\) | \(\Gamma_0(N)\)-optimal |
6400.t2 | 6400b2 | \([0, 1, 0, 417, -787]\) | \(1600\) | \(-5000000000\) | \([]\) | \(2880\) | \(0.55013\) |
Rank
sage: E.rank()
The elliptic curves in class 6400.t have rank \(1\).
Complex multiplication
The elliptic curves in class 6400.t do not have complex multiplication.Modular form 6400.2.a.t
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.