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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 954.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
954.c1 | 954e2 | \([1, -1, 0, -221427, 40159989]\) | \(-1646982616152408625/38112512\) | \(-27784021248\) | \([3]\) | \(4320\) | \(1.5267\) | |
954.c2 | 954e1 | \([1, -1, 0, -2547, 63477]\) | \(-2507141976625/889192448\) | \(-648221294592\) | \([]\) | \(1440\) | \(0.97740\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 954.c have rank \(1\).
Complex multiplication
The elliptic curves in class 954.c do not have complex multiplication.Modular form 954.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.