# Properties

 Label 1520.d Number of curves $2$ Conductor $1520$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("d1")

E.isogeny_class()

## Elliptic curves in class 1520.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1520.d1 1520j2 $$[0, -1, 0, -44480, 3625600]$$ $$-2376117230685121/342950$$ $$-1404723200$$ $$[]$$ $$1728$$ $$1.1643$$
1520.d2 1520j1 $$[0, -1, 0, -480, 6400]$$ $$-2992209121/2375000$$ $$-9728000000$$ $$[]$$ $$576$$ $$0.61498$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1520.2.a.d

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.