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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 91035g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
91035.bj4 | 91035g1 | \([1, -1, 0, -470835, 282717000]\) | \(-656008386769/1581036975\) | \(-27820381636122441975\) | \([2]\) | \(1769472\) | \(2.4191\) | \(\Gamma_0(N)\)-optimal |
91035.bj3 | 91035g2 | \([1, -1, 0, -9951480, 12074743251]\) | \(6193921595708449/6452105625\) | \(113533107499950980625\) | \([2, 2]\) | \(3538944\) | \(2.7657\) | |
91035.bj2 | 91035g3 | \([1, -1, 0, -12409425, 5655082500]\) | \(12010404962647729/6166198828125\) | \(108502209217876433203125\) | \([2]\) | \(7077888\) | \(3.1123\) | |
91035.bj1 | 91035g4 | \([1, -1, 0, -159183855, 773070316326]\) | \(25351269426118370449/27551475\) | \(484803683442056475\) | \([2]\) | \(7077888\) | \(3.1123\) |
Rank
sage: E.rank()
The elliptic curves in class 91035g have rank \(0\).
Complex multiplication
The elliptic curves in class 91035g do not have complex multiplication.Modular form 91035.2.a.g
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.