# Properties

 Label 1520.i Number of curves $2$ Conductor $1520$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("i1")

E.isogeny_class()

## Elliptic curves in class 1520.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1520.i1 1520a1 $$[0, -1, 0, -35, -58]$$ $$304900096/45125$$ $$722000$$ $$[2]$$ $$192$$ $$-0.15122$$ $$\Gamma_0(N)$$-optimal
1520.i2 1520a2 $$[0, -1, 0, 60, -400]$$ $$91765424/296875$$ $$-76000000$$ $$[2]$$ $$384$$ $$0.19535$$

## Rank

sage: E.rank()

The elliptic curves in class 1520.i have rank $$0$$.

## Complex multiplication

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

## Modular form1520.2.a.i

sage: E.q_eigenform(10)

$$q + 2 q^{3} + q^{5} + q^{9} + 4 q^{11} + 4 q^{13} + 2 q^{15} - 2 q^{17} - q^{19} + O(q^{20})$$

## 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.