Show commands:
SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 369600cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
369600.cc2 | 369600cc1 | \([0, -1, 0, -8232133, 12482799637]\) | \(-3856034557002072064/1973796785296875\) | \(-31580748564750000000000\) | \([2]\) | \(30965760\) | \(3.0219\) | \(\Gamma_0(N)\)-optimal |
369600.cc1 | 369600cc2 | \([0, -1, 0, -144919633, 671453237137]\) | \(1314817350433665559504/190690249278375\) | \(48816703815264000000000\) | \([2]\) | \(61931520\) | \(3.3685\) |
Rank
sage: E.rank()
The elliptic curves in class 369600cc have rank \(0\).
Complex multiplication
The elliptic curves in class 369600cc do not have complex multiplication.Modular form 369600.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.