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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 4900q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4900.l1 | 4900q1 | \([0, 0, 0, -3920, 94325]\) | \(28311552/49\) | \(11529602000\) | \([2]\) | \(3456\) | \(0.82463\) | \(\Gamma_0(N)\)-optimal |
4900.l2 | 4900q2 | \([0, 0, 0, -2695, 154350]\) | \(-574992/2401\) | \(-9039207968000\) | \([2]\) | \(6912\) | \(1.1712\) |
Rank
sage: E.rank()
The elliptic curves in class 4900q have rank \(0\).
Complex multiplication
The elliptic curves in class 4900q do not have complex multiplication.Modular form 4900.2.a.q
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.