Properties

Label 37030r
Number of curves $4$
Conductor $37030$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 37030r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37030.p4 37030r1 \([1, 0, 0, -973900, -368430000]\) \(690080604747409/3406760000\) \(504322745209640000\) \([2]\) \(1317888\) \(2.2445\) \(\Gamma_0(N)\)-optimal
37030.p3 37030r2 \([1, 0, 0, -1502900, 75824200]\) \(2535986675931409/1450751712200\) \(214763319433799145800\) \([2]\) \(2635776\) \(2.5911\)  
37030.p2 37030r3 \([1, 0, 0, -5597360, 4830723772]\) \(131010595463836369/7704101562500\) \(1140483523750976562500\) \([2]\) \(3953664\) \(2.7938\)  
37030.p1 37030r4 \([1, 0, 0, -88253610, 319106317522]\) \(513516182162686336369/1944885031250\) \(287912784603886531250\) \([2]\) \(7907328\) \(3.1404\)  

Rank

sage: E.rank()
 

The elliptic curves in class 37030r have rank \(0\).

Complex multiplication

The elliptic curves in class 37030r do not have complex multiplication.

Modular form 37030.2.a.r

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} + q^{4} + q^{5} - 2 q^{6} - q^{7} + q^{8} + q^{9} + q^{10} + 6 q^{11} - 2 q^{12} - 4 q^{13} - q^{14} - 2 q^{15} + q^{16} - 6 q^{17} + q^{18} - 8 q^{19} + O(q^{20})\) 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 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.