# Properties

 Label 229320.eh Number of curves $2$ Conductor $229320$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("eh1")

sage: E.isogeny_class()

## Elliptic curves in class 229320.eh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.eh1 229320em1 $$[0, 0, 0, -56742, 5194049]$$ $$397526095872/739375$$ $$37578267090000$$ $$$$ $$688128$$ $$1.4955$$ $$\Gamma_0(N)$$-optimal
229320.eh2 229320em2 $$[0, 0, 0, -38367, 8615474]$$ $$-7680778992/34987225$$ $$-28451257579180800$$ $$$$ $$1376256$$ $$1.8420$$

## Rank

sage: E.rank()

The elliptic curves in class 229320.eh have rank $$1$$.

## Complex multiplication

The elliptic curves in class 229320.eh do not have complex multiplication.

## Modular form 229320.2.a.eh

sage: E.q_eigenform(10)

$$q + q^{5} + 2 q^{11} - q^{13} + 6 q^{17} + O(q^{20})$$ ## 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. 