Properties

Label 60840.bb
Number of curves $4$
Conductor $60840$
CM no
Rank $0$
Graph

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

Elliptic curves in class 60840.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60840.bb1 60840ca4 \([0, 0, 0, -12655227, -17328182794]\) \(31103978031362/195\) \(1405245508392960\) \([2]\) \(2064384\) \(2.5122\)  
60840.bb2 60840ca3 \([0, 0, 0, -1095627, -43417114]\) \(20183398562/11567205\) \(83357758312361994240\) \([2]\) \(2064384\) \(2.5122\)  
60840.bb3 60840ca2 \([0, 0, 0, -791427, -270411154]\) \(15214885924/38025\) \(137011437068313600\) \([2, 2]\) \(1032192\) \(2.1656\)  
60840.bb4 60840ca1 \([0, 0, 0, -30927, -7430254]\) \(-3631696/24375\) \(-21956961068640000\) \([4]\) \(516096\) \(1.8190\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 60840.bb have rank \(0\).

Complex multiplication

The elliptic curves in class 60840.bb do not have complex multiplication.

Modular form 60840.2.a.bb

sage: E.q_eigenform(10)
 
\(q + q^{5} - 4q^{7} + 4q^{11} - 6q^{17} + O(q^{20})\)  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.