# Properties

 Label 1520.f Number of curves $4$ Conductor $1520$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("f1")

E.isogeny_class()

## Elliptic curves in class 1520.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1520.f1 1520b3 $$[0, 0, 0, -2027, -35126]$$ $$899466517764/95$$ $$97280$$ $$[2]$$ $$512$$ $$0.38532$$
1520.f2 1520b4 $$[0, 0, 0, -227, 434]$$ $$1263284964/651605$$ $$667243520$$ $$[4]$$ $$512$$ $$0.38532$$
1520.f3 1520b2 $$[0, 0, 0, -127, -546]$$ $$884901456/9025$$ $$2310400$$ $$[2, 2]$$ $$256$$ $$0.038746$$
1520.f4 1520b1 $$[0, 0, 0, -2, -21]$$ $$-55296/11875$$ $$-190000$$ $$[2]$$ $$128$$ $$-0.30783$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1520.f have rank $$1$$.

## Complex multiplication

The elliptic curves in class 1520.f do not have complex multiplication.

## Modular form1520.2.a.f

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.