Properties

Label 318402do
Number of curves $4$
Conductor $318402$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("do1")
 
E.isogeny_class()
 

Elliptic curves in class 318402do

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
318402.do2 318402do1 \([1, -1, 1, -2471015105, 47278846173521]\) \(11165451838341046875/572244736\) \(85517582701982832269568\) \([2]\) \(159252480\) \(3.8732\) \(\Gamma_0(N)\)-optimal
318402.do3 318402do2 \([1, -1, 1, -2466769745, 47449392473585]\) \(-11108001800138902875/79947274872976\) \(-11947506478675374152497856688\) \([2]\) \(318504960\) \(4.2198\)  
318402.do1 318402do3 \([1, -1, 1, -2692039160, 38319083977339]\) \(19804628171203875/5638671302656\) \(614296324889388751092461862912\) \([2]\) \(477757440\) \(4.4225\)  
318402.do4 318402do4 \([1, -1, 1, 7089270280, 252772337187451]\) \(361682234074684125/462672528510976\) \(-50405143097753797544779443351552\) \([2]\) \(955514880\) \(4.7691\)  

Rank

sage: E.rank()
 

The elliptic curves in class 318402do have rank \(0\).

Complex multiplication

The elliptic curves in class 318402do do not have complex multiplication.

Modular form 318402.2.a.do

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{8} - 6 q^{11} + 2 q^{13} + q^{16} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.