# Properties

 Label 1520.e Number of curves $2$ Conductor $1520$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("e1")

E.isogeny_class()

## Elliptic curves in class 1520.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1520.e1 1520f2 $$[0, 0, 0, -103, 402]$$ $$472058064/475$$ $$121600$$ $$$$ $$192$$ $$-0.10516$$
1520.e2 1520f1 $$[0, 0, 0, -8, 3]$$ $$3538944/1805$$ $$28880$$ $$$$ $$96$$ $$-0.45173$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1520.2.a.e

sage: E.q_eigenform(10)

$$q - q^{5} + 2 q^{7} - 3 q^{9} + 4 q^{11} - 4 q^{13} + 6 q^{17} - q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 