# Properties

 Label 75150r Number of curves 2 Conductor 75150 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("75150.m1")

sage: E.isogeny_class()

## Elliptic curves in class 75150r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
75150.m1 75150r1 [1, -1, 0, -10242, 366916]  230400 $$\Gamma_0(N)$$-optimal
75150.m2 75150r2 [1, -1, 0, 12258, 1739416]  460800

## Rank

sage: E.rank()

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

## Modular form 75150.2.a.m

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{8} - 2q^{11} - 6q^{13} + q^{16} + 4q^{17} - 8q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels. 