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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 63175.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
63175.c1 | 63175l2 | \([0, -1, 1, -150359508, 932115477918]\) | \(-511416541770305536/214587319023035\) | \(-157741398044792826075546875\) | \([]\) | \(25920000\) | \(3.7349\) | |
63175.c2 | 63175l1 | \([0, -1, 1, -1898258, -5767937082]\) | \(-1029077364736/18960396875\) | \(-13937633985844091796875\) | \([]\) | \(5184000\) | \(2.9301\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 63175.c have rank \(0\).
Complex multiplication
The elliptic curves in class 63175.c do not have complex multiplication.Modular form 63175.2.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.