Properties

Label 3696.bb
Number of curves $4$
Conductor $3696$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 3696.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3696.bb1 3696z3 \([0, 1, 0, -1472072, -687941772]\) \(86129359107301290313/9166294368\) \(37545141731328\) \([2]\) \(46080\) \(2.0325\)  
3696.bb2 3696z2 \([0, 1, 0, -92232, -10716300]\) \(21184262604460873/216872764416\) \(888310843047936\) \([2, 2]\) \(23040\) \(1.6859\)  
3696.bb3 3696z4 \([0, 1, 0, -23112, -26337420]\) \(-333345918055753/72923718045024\) \(-298695549112418304\) \([2]\) \(46080\) \(2.0325\)  
3696.bb4 3696z1 \([0, 1, 0, -10312, 129908]\) \(29609739866953/15259926528\) \(62504659058688\) \([2]\) \(11520\) \(1.3393\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3696.bb have rank \(0\).

Complex multiplication

The elliptic curves in class 3696.bb do not have complex multiplication.

Modular form 3696.2.a.bb

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