# Properties

 Label 3520.p Number of curves $4$ Conductor $3520$ CM no Rank $0$ Graph

# Learn more

Show commands: SageMath
E = EllipticCurve("p1")

E.isogeny_class()

## Elliptic curves in class 3520.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3520.p1 3520e4 $$[0, 0, 0, -3788, 89712]$$ $$22930509321/6875$$ $$1802240000$$ $$[2]$$ $$2048$$ $$0.75406$$
3520.p2 3520e3 $$[0, 0, 0, -1868, -30352]$$ $$2749884201/73205$$ $$19190251520$$ $$[2]$$ $$2048$$ $$0.75406$$
3520.p3 3520e2 $$[0, 0, 0, -268, 1008]$$ $$8120601/3025$$ $$792985600$$ $$[2, 2]$$ $$1024$$ $$0.40748$$
3520.p4 3520e1 $$[0, 0, 0, 52, 112]$$ $$59319/55$$ $$-14417920$$ $$[2]$$ $$512$$ $$0.060908$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3520.2.a.p

sage: E.q_eigenform(10)

$$q - q^{5} - 3 q^{9} + q^{11} - 2 q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.