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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 227136q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
227136.fw3 | 227136q1 | \([0, 1, 0, -2084, -31290]\) | \(3241792/567\) | \(175155244992\) | \([2]\) | \(245760\) | \(0.87727\) | \(\Gamma_0(N)\)-optimal |
227136.fw2 | 227136q2 | \([0, 1, 0, -9689, 335271]\) | \(5088448/441\) | \(8718838861824\) | \([2, 2]\) | \(491520\) | \(1.2238\) | |
227136.fw1 | 227136q3 | \([0, 1, 0, -151649, 22679775]\) | \(2438569736/21\) | \(3321462423552\) | \([2]\) | \(983040\) | \(1.5704\) | |
227136.fw4 | 227136q4 | \([0, 1, 0, 10591, 1572351]\) | \(830584/7203\) | \(-1139261611278336\) | \([2]\) | \(983040\) | \(1.5704\) |
Rank
sage: E.rank()
The elliptic curves in class 227136q have rank \(1\).
Complex multiplication
The elliptic curves in class 227136q do not have complex multiplication.Modular form 227136.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.