# Properties

 Label 428400lv Number of curves 4 Conductor 428400 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("428400.lv1")

sage: E.isogeny_class()

## Elliptic curves in class 428400lv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
428400.lv4 428400lv1 [0, 0, 0, 50325, 7308250]  3145728 $$\Gamma_0(N)$$-optimal*
428400.lv3 428400lv2 [0, 0, 0, -399675, 79758250] [2, 2] 6291456 $$\Gamma_0(N)$$-optimal*
428400.lv1 428400lv3 [0, 0, 0, -6069675, 5755428250]  12582912 $$\Gamma_0(N)$$-optimal*
428400.lv2 428400lv4 [0, 0, 0, -1929675, -959111750]  12582912
*optimality has not been proved rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 428400lv1.

## Rank

sage: E.rank()

The elliptic curves in class 428400lv have rank $$0$$.

## Modular form 428400.2.a.lv

sage: E.q_eigenform(10)

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

## 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. 