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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 32490t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32490.m2 | 32490t1 | \([1, -1, 0, -7679079, -413058947]\) | \(212883113611/122880000\) | \(28906209076947886080000\) | \([2]\) | \(4669440\) | \(2.9994\) | \(\Gamma_0(N)\)-optimal |
32490.m1 | 32490t2 | \([1, -1, 0, -86694759, -309885871235]\) | \(306331959547531/900000000\) | \(211715398512801900000000\) | \([2]\) | \(9338880\) | \(3.3460\) |
Rank
sage: E.rank()
The elliptic curves in class 32490t have rank \(1\).
Complex multiplication
The elliptic curves in class 32490t do not have complex multiplication.Modular form 32490.2.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.