Properties

Label 15680.cb
Number of curves $4$
Conductor $15680$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15680.cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.cb1 15680di4 \([0, 0, 0, -2561132, 1577596944]\) \(481927184300808/1225\) \(4722524979200\) \([2]\) \(147456\) \(2.0956\)  
15680.cb2 15680di3 \([0, 0, 0, -209132, 8303344]\) \(262389836808/144120025\) \(555600341277900800\) \([2]\) \(147456\) \(2.0956\)  
15680.cb3 15680di2 \([0, 0, 0, -160132, 24630144]\) \(942344950464/1500625\) \(723136637440000\) \([2, 2]\) \(73728\) \(1.7490\)  
15680.cb4 15680di1 \([0, 0, 0, -7007, 620144]\) \(-5053029696/19140625\) \(-144120025000000\) \([2]\) \(36864\) \(1.4024\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 15680.cb have rank \(0\).

Complex multiplication

The elliptic curves in class 15680.cb do not have complex multiplication.

Modular form 15680.2.a.cb

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