Show commands:
SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 193830.cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193830.cc1 | 193830f2 | \([1, 0, 0, -97511805, -371006520105]\) | \(-102540468901688739487767312721/119848113393926474790870\) | \(-119848113393926474790870\) | \([]\) | \(45715040\) | \(3.3406\) | |
193830.cc2 | 193830f1 | \([1, 0, 0, 120345, 195518025]\) | \(192755882359997444879/16624047233430000000\) | \(-16624047233430000000\) | \([7]\) | \(6530720\) | \(2.3676\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 193830.cc have rank \(0\).
Complex multiplication
The elliptic curves in class 193830.cc do not have complex multiplication.Modular form 193830.2.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.