# Properties

 Label 381150.oh Number of curves $2$ Conductor $381150$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("oh1")

sage: E.isogeny_class()

## Elliptic curves in class 381150.oh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
381150.oh1 381150oh2 $$[1, -1, 1, -9542930, -12003000303]$$ $$-7620530425/526848$$ $$-6644602700505000000000$$ $$[]$$ $$27993600$$ $$2.9383$$
381150.oh2 381150oh1 $$[1, -1, 1, 666445, -17194053]$$ $$2595575/1512$$ $$-19069331729765625000$$ $$[]$$ $$9331200$$ $$2.3890$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 381150.oh have rank $$1$$.

## Complex multiplication

The elliptic curves in class 381150.oh do not have complex multiplication.

## Modular form 381150.2.a.oh

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{7} + q^{8} - q^{13} + q^{14} + q^{16} - 3q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.