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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 5610.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5610.t1 | 5610r4 | \([1, 0, 1, -2417353, -1087483252]\) | \(1562225332123379392365961/393363080510106009600\) | \(393363080510106009600\) | \([2]\) | \(276480\) | \(2.6617\) | |
5610.t2 | 5610r2 | \([1, 0, 1, -829978, 290863148]\) | \(63229930193881628103961/26218934428500000\) | \(26218934428500000\) | \([6]\) | \(92160\) | \(2.1124\) | |
5610.t3 | 5610r1 | \([1, 0, 1, -43898, 5987756]\) | \(-9354997870579612441/10093752054144000\) | \(-10093752054144000\) | \([6]\) | \(46080\) | \(1.7658\) | \(\Gamma_0(N)\)-optimal |
5610.t4 | 5610r3 | \([1, 0, 1, 367927, -108178804]\) | \(5508208700580085578359/8246033269590589440\) | \(-8246033269590589440\) | \([2]\) | \(138240\) | \(2.3151\) |
Rank
sage: E.rank()
The elliptic curves in class 5610.t have rank \(0\).
Complex multiplication
The elliptic curves in class 5610.t do not have complex multiplication.Modular form 5610.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.