# Properties

 Label 75150.h Number of curves 2 Conductor 75150 CM no Rank 2 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("75150.h1")

sage: E.isogeny_class()

## Elliptic curves in class 75150.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
75150.h1 75150i2 [1, -1, 0, -25255692, 48817755216]  5806080
75150.h2 75150i1 [1, -1, 0, -1207692, 1130571216]  2903040 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 75150.h have rank $$2$$.

## Modular form 75150.2.a.h

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - 2q^{7} - q^{8} - 2q^{13} + 2q^{14} + q^{16} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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. 