# Properties

 Label 114.c Number of curves $4$ Conductor $114$ CM no Rank $0$ Graph # Learn more

Show commands for: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 114.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
114.c1 114a3 $$[1, 0, 0, -428, -3444]$$ $$8671983378625/82308$$ $$82308$$ $$$$ $$36$$ $$0.10550$$
114.c2 114a4 $$[1, 0, 0, -418, -3610]$$ $$-8078253774625/846825858$$ $$-846825858$$ $$$$ $$72$$ $$0.45208$$
114.c3 114a1 $$[1, 0, 0, -8, 0]$$ $$57066625/32832$$ $$32832$$ $$$$ $$12$$ $$-0.44380$$ $$\Gamma_0(N)$$-optimal
114.c4 114a2 $$[1, 0, 0, 32, 8]$$ $$3616805375/2105352$$ $$-2105352$$ $$$$ $$24$$ $$-0.097231$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form114.2.a.c

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} - 4q^{7} + q^{8} + q^{9} + q^{12} - 4q^{13} - 4q^{14} + q^{16} + 6q^{17} + q^{18} + q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 