# Properties

 Label 75150.g Number of curves 2 Conductor 75150 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("75150.g1")

sage: E.isogeny_class()

## Elliptic curves in class 75150.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
75150.g1 75150c2 [1, -1, 0, -126942, 16977716] [2] 460800
75150.g2 75150c1 [1, -1, 0, -18942, -626284] [2] 230400 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 75150.g have rank $$1$$.

## Modular form 75150.2.a.g

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - 2q^{7} - q^{8} - 2q^{11} + 2q^{13} + 2q^{14} + q^{16} + 4q^{19} + O(q^{20})$$

## 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.