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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 46200t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46200.k2 | 46200t1 | \([0, -1, 0, -777243, -295924968]\) | \(-25963589461091772416/3923372657421063\) | \(-7846745314842126000\) | \([2]\) | \(806400\) | \(2.3550\) | \(\Gamma_0(N)\)-optimal |
46200.k1 | 46200t2 | \([0, -1, 0, -12856068, -17737748268]\) | \(7343418009347613339536/136478763980097\) | \(4367320447363104000\) | \([2]\) | \(1612800\) | \(2.7016\) |
Rank
sage: E.rank()
The elliptic curves in class 46200t have rank \(1\).
Complex multiplication
The elliptic curves in class 46200t do not have complex multiplication.Modular form 46200.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.