# Properties

 Label 3380.h Number of curves $2$ Conductor $3380$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 3380.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3380.h1 3380f2 $$[0, 1, 0, -85570, -9663107]$$ $$151635187115776/25$$ $$11424400$$ $$[]$$ $$5184$$ $$1.1971$$
3380.h2 3380f1 $$[0, 1, 0, -1070, -13207]$$ $$296747776/15625$$ $$7140250000$$ $$$$ $$1728$$ $$0.64776$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3380.2.a.h

sage: E.q_eigenform(10)

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

## 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. 