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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 858c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
858.b2 | 858c1 | \([1, 0, 1, -7, -10]\) | \(-30664297/18876\) | \(-18876\) | \([2]\) | \(80\) | \(-0.47764\) | \(\Gamma_0(N)\)-optimal |
858.b1 | 858c2 | \([1, 0, 1, -117, -494]\) | \(174958262857/33462\) | \(33462\) | \([2]\) | \(160\) | \(-0.13107\) |
Rank
sage: E.rank()
The elliptic curves in class 858c have rank \(0\).
Complex multiplication
The elliptic curves in class 858c do not have complex multiplication.Modular form 858.2.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.