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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 2210c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2210.e1 | 2210c1 | \([1, -1, 1, -18, 17]\) | \(611960049/282880\) | \(282880\) | \([2]\) | \(256\) | \(-0.25927\) | \(\Gamma_0(N)\)-optimal |
2210.e2 | 2210c2 | \([1, -1, 1, 62, 81]\) | \(26757728271/19536400\) | \(-19536400\) | \([2]\) | \(512\) | \(0.087299\) |
Rank
sage: E.rank()
The elliptic curves in class 2210c have rank \(1\).
Complex multiplication
The elliptic curves in class 2210c do not have complex multiplication.Modular form 2210.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.