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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 229320.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
229320.y1 | 229320cp1 | \([0, 0, 0, -510678, -140239323]\) | \(397526095872/739375\) | \(27394556708610000\) | \([2]\) | \(2064384\) | \(2.0448\) | \(\Gamma_0(N)\)-optimal |
229320.y2 | 229320cp2 | \([0, 0, 0, -345303, -232617798]\) | \(-7680778992/34987225\) | \(-20740966775222803200\) | \([2]\) | \(4128768\) | \(2.3913\) |
Rank
sage: E.rank()
The elliptic curves in class 229320.y have rank \(1\).
Complex multiplication
The elliptic curves in class 229320.y do not have complex multiplication.Modular form 229320.2.a.y
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.