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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 2800t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2800.y2 | 2800t1 | \([0, 1, 0, -133, 2863]\) | \(-65536/875\) | \(-3500000000\) | \([]\) | \(1152\) | \(0.51296\) | \(\Gamma_0(N)\)-optimal |
2800.y1 | 2800t2 | \([0, 1, 0, -20133, 1092863]\) | \(-225637236736/1715\) | \(-6860000000\) | \([]\) | \(3456\) | \(1.0623\) |
Rank
sage: E.rank()
The elliptic curves in class 2800t have rank \(1\).
Complex multiplication
The elliptic curves in class 2800t do not have complex multiplication.Modular form 2800.2.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 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.