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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 270480q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
270480.q2 | 270480q1 | \([0, -1, 0, -17857576, -1994170109840]\) | \(-1306902141891515161/3564268498800000000\) | \(-1717586430424355635200000000\) | \([2]\) | \(149299200\) | \(3.9048\) | \(\Gamma_0(N)\)-optimal |
270480.q1 | 270480q2 | \([0, -1, 0, -2486893096, -47136040329104]\) | \(3529773792266261468365081/50841342773437500000\) | \(24499950124860000000000000000\) | \([2]\) | \(298598400\) | \(4.2514\) |
Rank
sage: E.rank()
The elliptic curves in class 270480q have rank \(0\).
Complex multiplication
The elliptic curves in class 270480q do not have complex multiplication.Modular form 270480.2.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.