# Properties

 Label 3640.h Number of curves $2$ Conductor $3640$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 3640.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3640.h1 3640d1 $$[0, -1, 0, -476, 3860]$$ $$46689225424/3901625$$ $$998816000$$ $$$$ $$2304$$ $$0.46879$$ $$\Gamma_0(N)$$-optimal
3640.h2 3640d2 $$[0, -1, 0, 504, 16796]$$ $$13799183324/129390625$$ $$-132496000000$$ $$$$ $$4608$$ $$0.81536$$

## Rank

sage: E.rank()

The elliptic curves in class 3640.h have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3640.h do not have complex multiplication.

## Modular form3640.2.a.h

sage: E.q_eigenform(10)

$$q + 2 q^{3} - q^{5} + q^{7} + q^{9} + 6 q^{11} - q^{13} - 2 q^{15} - 2 q^{17} + 2 q^{19} + O(q^{20})$$

## 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. 