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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 43560.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43560.x1 | 43560bp1 | \([0, 0, 0, -61743, 5905042]\) | \(104795188976/1875\) | \(465743520000\) | \([2]\) | \(122880\) | \(1.3659\) | \(\Gamma_0(N)\)-optimal |
43560.x2 | 43560bp2 | \([0, 0, 0, -59763, 6301438]\) | \(-23758298924/3515625\) | \(-3493076400000000\) | \([2]\) | \(245760\) | \(1.7124\) |
Rank
sage: E.rank()
The elliptic curves in class 43560.x have rank \(1\).
Complex multiplication
The elliptic curves in class 43560.x do not have complex multiplication.Modular form 43560.2.a.x
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.