Properties

Label 23400.r
Number of curves $2$
Conductor $23400$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 23400.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23400.r1 23400p2 \([0, 0, 0, -15375, 733250]\) \(137842000/117\) \(341172000000\) \([2]\) \(36864\) \(1.1402\)  
23400.r2 23400p1 \([0, 0, 0, -750, 16625]\) \(-256000/507\) \(-92400750000\) \([2]\) \(18432\) \(0.79359\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 23400.r have rank \(1\).

Complex multiplication

The elliptic curves in class 23400.r do not have complex multiplication.

Modular form 23400.2.a.r

sage: E.q_eigenform(10)
 
\(q - 6 q^{11} + q^{13} + 2 q^{17} + O(q^{20})\) 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.