Properties

Label 3380.g
Number of curves $2$
Conductor $3380$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3380.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3380.g1 3380a2 \([0, 1, 0, -14461386, -21172000615]\) \(151635187115776/25\) \(55143396739600\) \([]\) \(67392\) \(2.4795\)  
3380.g2 3380a1 \([0, 1, 0, -180886, -28292315]\) \(296747776/15625\) \(34464622962250000\) \([]\) \(22464\) \(1.9302\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3380.g have rank \(0\).

Complex multiplication

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

Modular form 3380.2.a.g

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.