Properties

Label 273600.cg
Number of curves $2$
Conductor $273600$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("cg1")
 
E.isogeny_class()
 

Elliptic curves in class 273600.cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
273600.cg1 273600cg2 \([0, 0, 0, -7800300, 8304498000]\) \(651038076963/7220000\) \(582087720960000000000\) \([2]\) \(17694720\) \(2.7988\)  
273600.cg2 273600cg1 \([0, 0, 0, -888300, -114318000]\) \(961504803/486400\) \(39214330675200000000\) \([2]\) \(8847360\) \(2.4522\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 273600.cg have rank \(0\).

Complex multiplication

The elliptic curves in class 273600.cg do not have complex multiplication.

Modular form 273600.2.a.cg

sage: E.q_eigenform(10)
 
\(q - 4 q^{7} + 6 q^{11} + 4 q^{17} - q^{19} + O(q^{20})\) Copy content 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.