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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 25350g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25350.v4 | 25350g1 | \([1, 1, 0, -1219000, 855304000]\) | \(-2656166199049/2658140160\) | \(-200473981992960000000\) | \([2]\) | \(1290240\) | \(2.5913\) | \(\Gamma_0(N)\)-optimal |
25350.v3 | 25350g2 | \([1, 1, 0, -22851000, 42021000000]\) | \(17496824387403529/6580454400\) | \(496290570656400000000\) | \([2, 2]\) | \(2580480\) | \(2.9379\) | |
25350.v2 | 25350g3 | \([1, 1, 0, -26231000, 28768020000]\) | \(26465989780414729/10571870144160\) | \(797318718104106022500000\) | \([2]\) | \(5160960\) | \(3.2845\) | |
25350.v1 | 25350g4 | \([1, 1, 0, -365583000, 2690311164000]\) | \(71647584155243142409/10140000\) | \(764747550937500000\) | \([2]\) | \(5160960\) | \(3.2845\) |
Rank
sage: E.rank()
The elliptic curves in class 25350g have rank \(1\).
Complex multiplication
The elliptic curves in class 25350g do not have complex multiplication.Modular form 25350.2.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.