# Properties

 Label 1520i Number of curves $2$ Conductor $1520$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1520i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1520.b1 1520i1 $$[0, 1, 0, -921, -10346]$$ $$5405726654464/407253125$$ $$6516050000$$ $$$$ $$960$$ $$0.62837$$ $$\Gamma_0(N)$$-optimal
1520.b2 1520i2 $$[0, 1, 0, 884, -44280]$$ $$298091207216/3525390625$$ $$-902500000000$$ $$$$ $$1920$$ $$0.97495$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1520.2.a.i

sage: E.q_eigenform(10)

$$q - 2 q^{3} - q^{5} - 2 q^{7} + q^{9} + 6 q^{13} + 2 q^{15} + 2 q^{17} + q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels. 