↑

Properties

Label 60690.b
Number of curves $4$
Conductor $60690$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 60690.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60690.b1 60690c4 \([1, 1, 0, -54520578, -131853357468]\) \(742525803457216841161/118657634071410000\) \(2864106829775409802290000\) \([2]\) \(17694720\) \(3.4153\)  
60690.b2 60690c2 \([1, 1, 0, -15193458, 20806656948]\) \(16069416876629693641/1546622367494400\) \(37331704112339437113600\) \([2, 2]\) \(8847360\) \(3.0687\)  
60690.b3 60690c1 \([1, 1, 0, -14823538, 21960881332]\) \(14924020698027934921/161083883520\) \(3888173353251962880\) \([2]\) \(4423680\) \(2.7221\) \(\Gamma_0(N)\)-optimal
60690.b4 60690c3 \([1, 1, 0, 18214942, 99603709188]\) \(27689398696638536759/193555307298039120\) \(-4671954585222622823699280\) \([2]\) \(17694720\) \(3.4153\)  

Rank

sage: E.rank()
 

The elliptic curves in class 60690.b have rank \(1\).

Complex multiplication

The elliptic curves in class 60690.b do not have complex multiplication.

Modular form 60690.2.a.b

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.