# Properties

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

# Related objects

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 form3420.2.a.f

sage: E.q_eigenform(10)

$$q + q^{5} + 2 q^{7} + 6 q^{13} - 2 q^{17} - q^{19} + O(q^{20})$$

## 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.