# Properties

 Label 9576v Number of curves $4$ Conductor $9576$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("v1")

E.isogeny_class()

## Elliptic curves in class 9576v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9576.t4 9576v1 $$[0, 0, 0, -39234, 1171613]$$ $$572616640141312/280535480757$$ $$3272165847549648$$ $$[2]$$ $$49152$$ $$1.6703$$ $$\Gamma_0(N)$$-optimal
9576.t2 9576v2 $$[0, 0, 0, -334479, -73643470]$$ $$22174957026242512/278654127129$$ $$52003547821322496$$ $$[2, 2]$$ $$98304$$ $$2.0169$$
9576.t1 9576v3 $$[0, 0, 0, -5335419, -4743521242]$$ $$22501000029889239268/3620708343$$ $$2702844295216128$$ $$[2]$$ $$196608$$ $$2.3635$$
9576.t3 9576v4 $$[0, 0, 0, -57459, -191931010]$$ $$-28104147578308/21301741002339$$ $$-15901664451282054144$$ $$[2]$$ $$196608$$ $$2.3635$$

## Rank

sage: E.rank()

The elliptic curves in class 9576v have rank $$0$$.

## Complex multiplication

The elliptic curves in class 9576v do not have complex multiplication.

## Modular form9576.2.a.v

sage: E.q_eigenform(10)

$$q + 2 q^{5} - q^{7} + 4 q^{11} + 2 q^{13} + 6 q^{17} + q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.