# Properties

 Label 3380.i Number of curves $2$ Conductor $3380$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 3380.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3380.i1 3380e2 $$[0, 1, 0, -290, -1975]$$ $$1000939264/15625$$ $$42250000$$ $$[]$$ $$864$$ $$0.26419$$
3380.i2 3380e1 $$[0, 1, 0, -30, 53]$$ $$1141504/25$$ $$67600$$ $$[]$$ $$288$$ $$-0.28511$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3380.i have rank $$1$$.

## Complex multiplication

The elliptic curves in class 3380.i do not have complex multiplication.

## Modular form3380.2.a.i

sage: E.q_eigenform(10)

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

## 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.