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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 17424.cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17424.cc1 | 17424cb2 | \([0, 0, 0, -7491, 256322]\) | \(-128667913/4096\) | \(-1479901446144\) | \([]\) | \(27648\) | \(1.1112\) | |
17424.cc2 | 17424cb1 | \([0, 0, 0, 429, 1298]\) | \(24167/16\) | \(-5780865024\) | \([]\) | \(9216\) | \(0.56194\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17424.cc have rank \(0\).
Complex multiplication
The elliptic curves in class 17424.cc do not have complex multiplication.Modular form 17424.2.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 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.