# Properties

 Label 424830.t Number of curves $2$ Conductor $424830$ CM no Rank $1$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("t1")

sage: E.isogeny_class()

## Elliptic curves in class 424830.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
424830.t1 424830t1 $$[1, 1, 0, -33198, 2377908]$$ $$-5831629329001/186624000$$ $$-129496340736000$$ $$[]$$ $$2309472$$ $$1.4837$$ $$\Gamma_0(N)$$-optimal
424830.t2 424830t2 $$[1, 1, 0, 154227, 8862813]$$ $$584669638645799/386547056640$$ $$-268220750584872960$$ $$[]$$ $$6928416$$ $$2.0330$$

## Rank

sage: E.rank()

The elliptic curves in class 424830.t have rank $$1$$.

## Complex multiplication

The elliptic curves in class 424830.t do not have complex multiplication.

## Modular form 424830.2.a.t

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} + 3q^{11} - q^{12} + 2q^{13} + q^{15} + q^{16} - q^{18} + 5q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 