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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 35520cj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35520.s1 | 35520cj1 | \([0, -1, 0, -30725, 2083125]\) | \(3132662187311104/151723125\) | \(155364480000\) | \([2]\) | \(86016\) | \(1.2201\) | \(\Gamma_0(N)\)-optimal |
35520.s2 | 35520cj2 | \([0, -1, 0, -29105, 2310897]\) | \(-166426126492624/43316015625\) | \(-709689600000000\) | \([2]\) | \(172032\) | \(1.5667\) |
Rank
sage: E.rank()
The elliptic curves in class 35520cj have rank \(2\).
Complex multiplication
The elliptic curves in class 35520cj do not have complex multiplication.Modular form 35520.2.a.cj
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.