# Properties

 Label 9025c Number of curves $3$ Conductor $9025$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 9025c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9025.d3 9025c1 $$[0, 1, 1, 6017, 9944]$$ $$32768/19$$ $$-13966745921875$$ $$[]$$ $$12960$$ $$1.2118$$ $$\Gamma_0(N)$$-optimal
9025.d2 9025c2 $$[0, 1, 1, -84233, 9982569]$$ $$-89915392/6859$$ $$-5041995277796875$$ $$[]$$ $$38880$$ $$1.7611$$
9025.d1 9025c3 $$[0, 1, 1, -6943233, 7039600194]$$ $$-50357871050752/19$$ $$-13966745921875$$ $$[]$$ $$116640$$ $$2.3104$$

## Rank

sage: E.rank()

The elliptic curves in class 9025c have rank $$0$$.

## Complex multiplication

The elliptic curves in class 9025c do not have complex multiplication.

## Modular form9025.2.a.c

sage: E.q_eigenform(10)

$$q - 2q^{3} - 2q^{4} + q^{7} + q^{9} + 3q^{11} + 4q^{12} - 4q^{13} + 4q^{16} + 3q^{17} + O(q^{20})$$

## 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.