# Properties

 Label 3024.p Number of curves $3$ Conductor $3024$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("p1")

E.isogeny_class()

## Elliptic curves in class 3024.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3024.p1 3024m3 $$[0, 0, 0, -152955, 23024682]$$ $$-545407363875/14$$ $$-10158317568$$ $$[]$$ $$7776$$ $$1.4363$$
3024.p2 3024m2 $$[0, 0, 0, -1755, 36234]$$ $$-7414875/2744$$ $$-221225582592$$ $$[]$$ $$2592$$ $$0.88703$$
3024.p3 3024m1 $$[0, 0, 0, 165, -502]$$ $$4492125/3584$$ $$-396361728$$ $$[]$$ $$864$$ $$0.33772$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3024.p have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3024.p do not have complex multiplication.

## Modular form3024.2.a.p

sage: E.q_eigenform(10)

$$q - q^{7} + 5 q^{13} + 3 q^{17} - 2 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 