# Properties

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

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("75150.o1")

sage: E.isogeny_class()

## Elliptic curves in class 75150l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
75150.o2 75150l1 [1, -1, 0, -11367, 580041] [2] 221184 $$\Gamma_0(N)$$-optimal
75150.o1 75150l2 [1, -1, 0, -193617, 32838291] [2] 442368

## Rank

sage: E.rank()

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

## Modular form 75150.2.a.o

sage: E.q_eigenform(10)

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

## 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 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.