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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 288834.cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
288834.cc1 | 288834cc2 | \([1, 0, 0, -1943808395, 32985734652723]\) | \(-5486773802537974663600129/2635437714\) | \(-390139364896117746\) | \([]\) | \(102685968\) | \(3.6143\) | |
288834.cc2 | 288834cc1 | \([1, 0, 0, 377695, 1009497033]\) | \(40251338884511/2997011332224\) | \(-443665236908854187136\) | \([]\) | \(14669424\) | \(2.6413\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 288834.cc have rank \(0\).
Complex multiplication
The elliptic curves in class 288834.cc do not have complex multiplication.Modular form 288834.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.