# Properties

 Label 2450.l Number of curves $4$ Conductor $2450$ CM no Rank $0$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 2450.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2450.l1 2450e4 [1, -1, 0, -327917, 72354491] [2] 18432
2450.l2 2450e3 [1, -1, 0, -107417, -12636009] [2] 18432
2450.l3 2450e2 [1, -1, 0, -21667, 998241] [2, 2] 9216
2450.l4 2450e1 [1, -1, 0, 2833, 91741] [2] 4608 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2450.l have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2450.l do not have complex multiplication.

## Modular form2450.2.a.l

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{8} - 3q^{9} + 4q^{11} - 6q^{13} + q^{16} + 2q^{17} + 3q^{18} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.