# Properties

 Label 234.d Number of curves $2$ Conductor $234$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("d1")

E.isogeny_class()

## Elliptic curves in class 234.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
234.d1 234b2 $$[1, -1, 1, -569, -5075]$$ $$1033364331/676$$ $$13305708$$ $$[2]$$ $$96$$ $$0.30665$$
234.d2 234b1 $$[1, -1, 1, -29, -107]$$ $$-132651/208$$ $$-4094064$$ $$[2]$$ $$48$$ $$-0.039925$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 234.d have rank $$0$$.

## Complex multiplication

The elliptic curves in class 234.d do not have complex multiplication.

## Modular form234.2.a.d

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 2 q^{5} - 2 q^{7} + q^{8} + 2 q^{10} + 4 q^{11} - q^{13} - 2 q^{14} + q^{16} - 6 q^{19} + O(q^{20})$$

## 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.