Show commands:
SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 155526cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
155526.bb2 | 155526cc1 | \([1, 0, 1, -2372312, 12578150]\) | \(6967871/4032\) | \(854396159776832683584\) | \([2]\) | \(7630848\) | \(2.7059\) | \(\Gamma_0(N)\)-optimal |
155526.bb1 | 155526cc2 | \([1, 0, 1, -26219632, 51522789350]\) | \(9407293631/31752\) | \(6728369758242557383224\) | \([2]\) | \(15261696\) | \(3.0525\) |
Rank
sage: E.rank()
The elliptic curves in class 155526cc have rank \(0\).
Complex multiplication
The elliptic curves in class 155526cc do not have complex multiplication.Modular form 155526.2.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.