# Properties

 Label 35728.m Number of curves $4$ Conductor $35728$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 35728.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35728.m1 35728y4 $$[0, 0, 0, -853691, -303564886]$$ $$16798320881842096017/2132227789307$$ $$8733605025001472$$ $$$$ $$344064$$ $$2.0807$$
35728.m2 35728y3 $$[0, 0, 0, -338651, 72754890]$$ $$1048626554636928177/48569076788309$$ $$198938938524913664$$ $$$$ $$344064$$ $$2.0807$$
35728.m3 35728y2 $$[0, 0, 0, -57931, -3881670]$$ $$5249244962308257/1448621666569$$ $$5933554346266624$$ $$[2, 2]$$ $$172032$$ $$1.7341$$
35728.m4 35728y1 $$[0, 0, 0, 9349, -396566]$$ $$22062729659823/29354283343$$ $$-120235144572928$$ $$$$ $$86016$$ $$1.3875$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 35728.m have rank $$1$$.

## Complex multiplication

The elliptic curves in class 35728.m do not have complex multiplication.

## Modular form 35728.2.a.m

sage: E.q_eigenform(10)

$$q - 2q^{5} + q^{7} - 3q^{9} + q^{11} + 6q^{13} - 2q^{17} + 8q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 