Show commands:
SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 22050.cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22050.cc1 | 22050e2 | \([1, -1, 0, -403692, -98622784]\) | \(68971442301/400\) | \(42195431250000\) | \([2]\) | \(147456\) | \(1.8047\) | |
22050.cc2 | 22050e1 | \([1, -1, 0, -25692, -1476784]\) | \(17779581/1280\) | \(135025380000000\) | \([2]\) | \(73728\) | \(1.4581\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22050.cc have rank \(0\).
Complex multiplication
The elliptic curves in class 22050.cc do not have complex multiplication.Modular form 22050.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.