# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 1520.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1520.c1 1520d2 $$[0, 1, 0, -20, -20]$$ $$3631696/1805$$ $$462080$$ $$$$ $$256$$ $$-0.22008$$
1520.c2 1520d1 $$[0, 1, 0, 5, 0]$$ $$702464/475$$ $$-7600$$ $$$$ $$128$$ $$-0.56666$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1520.2.a.c

sage: E.q_eigenform(10)

$$q - 2 q^{3} + q^{5} - 4 q^{7} + q^{9} + 4 q^{11} - 2 q^{15} + 6 q^{17} + q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 