# Properties

 Label 7440.q Number of curves $4$ Conductor $7440$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 7440.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7440.q1 7440u3 $$[0, 1, 0, -106056, -13329036]$$ $$32208729120020809/658986840$$ $$2699210096640$$ $$$$ $$27648$$ $$1.5049$$
7440.q2 7440u2 $$[0, 1, 0, -6856, -194956]$$ $$8702409880009/1120910400$$ $$4591248998400$$ $$[2, 2]$$ $$13824$$ $$1.1583$$
7440.q3 7440u1 $$[0, 1, 0, -1736, 24180]$$ $$141339344329/17141760$$ $$70212648960$$ $$$$ $$6912$$ $$0.81173$$ $$\Gamma_0(N)$$-optimal
7440.q4 7440u4 $$[0, 1, 0, 10424, -1003660]$$ $$30579142915511/124675335000$$ $$-510670172160000$$ $$$$ $$27648$$ $$1.5049$$

## Rank

sage: E.rank()

The elliptic curves in class 7440.q have rank $$0$$.

## Complex multiplication

The elliptic curves in class 7440.q do not have complex multiplication.

## Modular form7440.2.a.q

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 