↑

Properties

Label 175350.p
Number of curves $4$
Conductor $175350$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 175350.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
175350.p1 175350bv4 \([1, 0, 1, -5457726, -4907898152]\) \(1150638118585800835537/31752757008504\) \(496136828257875000\) \([2]\) \(8257536\) \(2.4986\)  
175350.p2 175350bv3 \([1, 0, 1, -1523726, 654525848]\) \(25039399590518087377/2641281025170312\) \(41270016018286125000\) \([2]\) \(8257536\) \(2.4986\)  
175350.p3 175350bv2 \([1, 0, 1, -354726, -70254152]\) \(315922815546536017/46479778841664\) \(726246544401000000\) \([2, 2]\) \(4128768\) \(2.1520\)  
175350.p4 175350bv1 \([1, 0, 1, 37274, -5966152]\) \(366554400441263/1197281046528\) \(-18707516352000000\) \([2]\) \(2064384\) \(1.8055\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 175350.p have rank \(1\).

Complex multiplication

The elliptic curves in class 175350.p do not have complex multiplication.

Modular form 175350.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + q^{9} - 4 q^{11} + q^{12} - 6 q^{13} + q^{14} + q^{16} + 2 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.