# Properties

 Label 3520.s Number of curves $2$ Conductor $3520$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("s1")

E.isogeny_class()

## Elliptic curves in class 3520.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3520.s1 3520i2 $$[0, 0, 0, -92, -304]$$ $$5256144/605$$ $$9912320$$ $$[2]$$ $$512$$ $$0.074505$$
3520.s2 3520i1 $$[0, 0, 0, 8, -24]$$ $$55296/275$$ $$-281600$$ $$[2]$$ $$256$$ $$-0.27207$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3520.s have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3520.s do not have complex multiplication.

## Modular form3520.2.a.s

sage: E.q_eigenform(10)

$$q + q^{5} - 2 q^{7} - 3 q^{9} - q^{11} + 4 q^{13} - 4 q^{17} + O(q^{20})$$

## 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.