# Properties

 Label 143745g Number of curves $4$ Conductor $143745$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 143745g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
143745.j3 143745g1 [1, 0, 0, -3451, 73640]  207360 $$\Gamma_0(N)$$-optimal
143745.j2 143745g2 [1, 0, 0, -10296, -311049] [2, 2] 414720
143745.j4 143745g3 [1, 0, 0, 23929, -1933314]  829440
143745.j1 143745g4 [1, 0, 0, -154041, -23281500]  829440

## Rank

sage: E.rank()

The elliptic curves in class 143745g have rank $$1$$.

## Complex multiplication

The elliptic curves in class 143745g do not have complex multiplication.

## Modular form 143745.2.a.g

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} - q^{4} - q^{5} - q^{6} + q^{7} + 3q^{8} + q^{9} + q^{10} - q^{12} + 6q^{13} - q^{14} - q^{15} - q^{16} - 2q^{17} - q^{18} + 8q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 