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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 11200.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11200.t1 | 11200cy2 | \([0, -1, 0, -593, -5393]\) | \(-2887553024/16807\) | \(-134456000\) | \([]\) | \(3200\) | \(0.40077\) | |
11200.t2 | 11200cy1 | \([0, -1, 0, 7, 7]\) | \(4096/7\) | \(-56000\) | \([]\) | \(640\) | \(-0.40395\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11200.t have rank \(1\).
Complex multiplication
The elliptic curves in class 11200.t do not have complex multiplication.Modular form 11200.2.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.