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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 18810c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18810.d1 | 18810c1 | \([1, -1, 0, -4365, -110075]\) | \(-12618417497041/20900000\) | \(-15236100000\) | \([]\) | \(24000\) | \(0.84998\) | \(\Gamma_0(N)\)-optimal |
18810.d2 | 18810c2 | \([1, -1, 0, 31185, 1487695]\) | \(4600717801439759/3987782200490\) | \(-2907093224157210\) | \([]\) | \(120000\) | \(1.6547\) |
Rank
sage: E.rank()
The elliptic curves in class 18810c have rank \(0\).
Complex multiplication
The elliptic curves in class 18810c do not have complex multiplication.Modular form 18810.2.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 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.