Properties

Label 3420.f
Number of curves $2$
Conductor $3420$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3420.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3420.f1 3420a1 \([0, 0, 0, -8292, -271051]\) \(5405726654464/407253125\) \(4750200450000\) \([2]\) \(5760\) \(1.1777\) \(\Gamma_0(N)\)-optimal
3420.f2 3420a2 \([0, 0, 0, 7953, -1203514]\) \(298091207216/3525390625\) \(-657922500000000\) \([2]\) \(11520\) \(1.5243\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3420.f have rank \(0\).

Complex multiplication

The elliptic curves in class 3420.f do not have complex multiplication.

Modular form 3420.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{5} + 2 q^{7} + 6 q^{13} - 2 q^{17} - q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.