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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 2090.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2090.g1 | 2090f4 | \([1, -1, 0, -5422064, 4860894720]\) | \(17628594000102642361428441/248187500000000\) | \(248187500000000\) | \([4]\) | \(36864\) | \(2.3162\) | |
2090.g2 | 2090f3 | \([1, -1, 0, -499184, -2880512]\) | \(13756443594716753103321/7957003087464992000\) | \(7957003087464992000\) | \([2]\) | \(36864\) | \(2.3162\) | |
2090.g3 | 2090f2 | \([1, -1, 0, -339184, 75871488]\) | \(4315493878427398863321/16147293184000000\) | \(16147293184000000\) | \([2, 2]\) | \(18432\) | \(1.9696\) | |
2090.g4 | 2090f1 | \([1, -1, 0, -11504, 2274560]\) | \(-168380411424176601/2131914391552000\) | \(-2131914391552000\) | \([2]\) | \(9216\) | \(1.6230\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2090.g have rank \(0\).
Complex multiplication
The elliptic curves in class 2090.g do not have complex multiplication.Modular form 2090.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.