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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 301530u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
301530.u4 | 301530u1 | \([1, 0, 1, -152099, 104255966]\) | \(-2628643361401/30205440000\) | \(-4471489163036160000\) | \([2]\) | \(7299072\) | \(2.2606\) | \(\Gamma_0(N)\)-optimal |
301530.u3 | 301530u2 | \([1, 0, 1, -4384099, 3522019166]\) | \(62950272087713401/222746241600\) | \(32974437896664782400\) | \([2, 2]\) | \(14598144\) | \(2.6072\) | |
301530.u1 | 301530u3 | \([1, 0, 1, -70085899, 225830629646]\) | \(257186774914508158201/3237173640\) | \(479217877644765960\) | \([2]\) | \(29196288\) | \(2.9538\) | |
301530.u2 | 301530u4 | \([1, 0, 1, -6394299, -32818514]\) | \(195314919505860601/113026425469560\) | \(16731967374878557038840\) | \([2]\) | \(29196288\) | \(2.9538\) |
Rank
sage: E.rank()
The elliptic curves in class 301530u have rank \(1\).
Complex multiplication
The elliptic curves in class 301530u do not have complex multiplication.Modular form 301530.2.a.u
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.