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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 8925t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8925.x4 | 8925t1 | \([1, 0, 1, -4526, -266677]\) | \(-656008386769/1581036975\) | \(-24703702734375\) | \([2]\) | \(18432\) | \(1.2580\) | \(\Gamma_0(N)\)-optimal |
8925.x3 | 8925t2 | \([1, 0, 1, -95651, -11383927]\) | \(6193921595708449/6452105625\) | \(100814150390625\) | \([2, 2]\) | \(36864\) | \(1.6045\) | |
8925.x1 | 8925t3 | \([1, 0, 1, -1530026, -728571427]\) | \(25351269426118370449/27551475\) | \(430491796875\) | \([2]\) | \(73728\) | \(1.9511\) | |
8925.x2 | 8925t4 | \([1, 0, 1, -119276, -5335927]\) | \(12010404962647729/6166198828125\) | \(96346856689453125\) | \([2]\) | \(73728\) | \(1.9511\) |
Rank
sage: E.rank()
The elliptic curves in class 8925t have rank \(1\).
Complex multiplication
The elliptic curves in class 8925t do not have complex multiplication.Modular form 8925.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.