Properties

Label 3380.c
Number of curves $4$
Conductor $3380$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3380.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3380.c1 3380i3 \([0, 1, 0, -6985, -226992]\) \(488095744/125\) \(9653618000\) \([2]\) \(3456\) \(0.90183\)  
3380.c2 3380i4 \([0, 1, 0, -6140, -283100]\) \(-20720464/15625\) \(-19307236000000\) \([2]\) \(6912\) \(1.2484\)  
3380.c3 3380i1 \([0, 1, 0, -225, 820]\) \(16384/5\) \(386144720\) \([2]\) \(1152\) \(0.35252\) \(\Gamma_0(N)\)-optimal
3380.c4 3380i2 \([0, 1, 0, 620, 6228]\) \(21296/25\) \(-30891577600\) \([2]\) \(2304\) \(0.69910\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3380.c have rank \(1\).

Complex multiplication

The elliptic curves in class 3380.c do not have complex multiplication.

Modular form 3380.2.a.c

sage: E.q_eigenform(10)
 
\(q - 2q^{3} + q^{5} - 2q^{7} + q^{9} - 2q^{15} - 6q^{17} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.