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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 56144q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
56144.r2 | 56144q1 | \([0, 1, 0, 9640, 608276]\) | \(13651919/29696\) | \(-215483496267776\) | \([]\) | \(129600\) | \(1.4345\) | \(\Gamma_0(N)\)-optimal |
56144.r1 | 56144q2 | \([0, 1, 0, -880920, -320690284]\) | \(-10418796526321/82044596\) | \(-595341338764722176\) | \([]\) | \(648000\) | \(2.2393\) |
Rank
sage: E.rank()
The elliptic curves in class 56144q have rank \(0\).
Complex multiplication
The elliptic curves in class 56144q do not have complex multiplication.Modular form 56144.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.