# Properties

 Label 14896bg Number of curves $3$ Conductor $14896$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bg1")

sage: E.isogeny_class()

## Elliptic curves in class 14896bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14896.a3 14896bg1 $$[0, 1, 0, 523, -29]$$ $$32768/19$$ $$-9155915776$$ $$[]$$ $$9072$$ $$0.60093$$ $$\Gamma_0(N)$$-optimal
14896.a2 14896bg2 $$[0, 1, 0, -7317, -258749]$$ $$-89915392/6859$$ $$-3305285595136$$ $$[]$$ $$27216$$ $$1.1502$$
14896.a1 14896bg3 $$[0, 1, 0, -603157, -180500349]$$ $$-50357871050752/19$$ $$-9155915776$$ $$[]$$ $$81648$$ $$1.6995$$

## Rank

sage: E.rank()

The elliptic curves in class 14896bg have rank $$0$$.

## Complex multiplication

The elliptic curves in class 14896bg do not have complex multiplication.

## Modular form 14896.2.a.bg

sage: E.q_eigenform(10)

$$q - 2q^{3} - 3q^{5} + q^{9} - 3q^{11} + 4q^{13} + 6q^{15} + 3q^{17} + q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.