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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 94640cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
94640.w2 | 94640cc1 | \([0, -1, 0, -901, 51401]\) | \(-65536/875\) | \(-1081205216000\) | \([]\) | \(112320\) | \(0.99072\) | \(\Gamma_0(N)\)-optimal |
94640.w1 | 94640cc2 | \([0, -1, 0, -136101, 19371481]\) | \(-225637236736/1715\) | \(-2119162223360\) | \([]\) | \(336960\) | \(1.5400\) |
Rank
sage: E.rank()
The elliptic curves in class 94640cc have rank \(1\).
Complex multiplication
The elliptic curves in class 94640cc do not have complex multiplication.Modular form 94640.2.a.cc
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.