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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 63075.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
63075.c1 | 63075v1 | \([0, 1, 1, -7008, -233806]\) | \(-102400/3\) | \(-1115293726875\) | \([]\) | \(134400\) | \(1.0905\) | \(\Gamma_0(N)\)-optimal |
63075.c2 | 63075v2 | \([0, 1, 1, 35042, 11161744]\) | \(20480/243\) | \(-56461744923046875\) | \([]\) | \(672000\) | \(1.8953\) |
Rank
sage: E.rank()
The elliptic curves in class 63075.c have rank \(1\).
Complex multiplication
The elliptic curves in class 63075.c do not have complex multiplication.Modular form 63075.2.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.