Properties

Label 135240.dq
Number of curves $2$
Conductor $135240$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("dq1")
 
E.isogeny_class()
 

Elliptic curves in class 135240.dq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
135240.dq1 135240ck2 \([0, 1, 0, -1188840, 433184688]\) \(264527137402013054/37471584403125\) \(26322439066156800000\) \([2]\) \(3317760\) \(2.4523\)  
135240.dq2 135240ck1 \([0, 1, 0, -313840, -61015312]\) \(9733205763526108/1069365234375\) \(375595290000000000\) \([2]\) \(1658880\) \(2.1057\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 135240.dq have rank \(0\).

Complex multiplication

The elliptic curves in class 135240.dq do not have complex multiplication.

Modular form 135240.2.a.dq

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} + 4 q^{11} + q^{15} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.