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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 18590.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18590.c1 | 18590b2 | \([1, 1, 0, -1003863, -387551237]\) | \(-23178622194826561/1610510\) | \(-7773624162590\) | \([]\) | \(192000\) | \(1.9275\) | |
18590.c2 | 18590b1 | \([1, 1, 0, 1687, -106907]\) | \(109902239/1100000\) | \(-5309489900000\) | \([]\) | \(38400\) | \(1.1228\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18590.c have rank \(1\).
Complex multiplication
The elliptic curves in class 18590.c do not have complex multiplication.Modular form 18590.2.a.c
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.