# Properties

 Label 114.a Number of curves $2$ Conductor $114$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 114.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
114.a1 114b1 $$[1, 1, 0, -95, -399]$$ $$96386901625/18468$$ $$18468$$ $$$$ $$20$$ $$-0.18069$$ $$\Gamma_0(N)$$-optimal
114.a2 114b2 $$[1, 1, 0, -85, -473]$$ $$-69173457625/42633378$$ $$-42633378$$ $$$$ $$40$$ $$0.16588$$

## Rank

sage: E.rank()

The elliptic curves in class 114.a have rank $$0$$.

## Complex multiplication

The elliptic curves in class 114.a do not have complex multiplication.

## Modular form114.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{6} + 4q^{7} - q^{8} + q^{9} + 4q^{11} - q^{12} - 4q^{14} + q^{16} - 2q^{17} - q^{18} + q^{19} + O(q^{20})$$ ## 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. 