Properties

Label 3380.i
Number of curves $2$
Conductor $3380$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3380.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3380.i1 3380e2 \([0, 1, 0, -290, -1975]\) \(1000939264/15625\) \(42250000\) \([]\) \(864\) \(0.26419\)  
3380.i2 3380e1 \([0, 1, 0, -30, 53]\) \(1141504/25\) \(67600\) \([]\) \(288\) \(-0.28511\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3380.2.a.i

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