Properties

Label 15680.cc
Number of curves $4$
Conductor $15680$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("cc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15680.cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.cc1 15680dk3 \([0, 0, 0, -20972, -1168944]\) \(132304644/5\) \(38551224320\) \([2]\) \(18432\) \(1.1173\)  
15680.cc2 15680dk2 \([0, 0, 0, -1372, -16464]\) \(148176/25\) \(48189030400\) \([2, 2]\) \(9216\) \(0.77074\)  
15680.cc3 15680dk1 \([0, 0, 0, -392, 2744]\) \(55296/5\) \(602362880\) \([2]\) \(4608\) \(0.42417\) \(\Gamma_0(N)\)-optimal
15680.cc4 15680dk4 \([0, 0, 0, 2548, -93296]\) \(237276/625\) \(-4818903040000\) \([2]\) \(18432\) \(1.1173\)  

Rank

sage: E.rank()
 

The elliptic curves in class 15680.cc have rank \(0\).

Complex multiplication

The elliptic curves in class 15680.cc do not have complex multiplication.

Modular form 15680.2.a.cc

sage: E.q_eigenform(10)
 
\(q + q^{5} - 3q^{9} + 4q^{11} - 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20})\)  Toggle raw display

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.