# Properties

 Label 25392.be Number of curves $6$ Conductor $25392$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("be1")

sage: E.isogeny_class()

## Elliptic curves in class 25392.be

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25392.be1 25392g6 $$[0, 1, 0, -203312, -35352972]$$ $$3065617154/9$$ $$2728597506048$$ $$[2]$$ $$90112$$ $$1.6155$$
25392.be2 25392g4 $$[0, 1, 0, -34032, 2404932]$$ $$28756228/3$$ $$454766251008$$ $$[2]$$ $$45056$$ $$1.2690$$
25392.be3 25392g3 $$[0, 1, 0, -12872, -540540]$$ $$1556068/81$$ $$12278688777216$$ $$[2, 2]$$ $$45056$$ $$1.2690$$
25392.be4 25392g2 $$[0, 1, 0, -2292, 30780]$$ $$35152/9$$ $$341074688256$$ $$[2, 2]$$ $$22528$$ $$0.92239$$
25392.be5 25392g1 $$[0, 1, 0, 353, 3272]$$ $$2048/3$$ $$-7105722672$$ $$[2]$$ $$11264$$ $$0.57582$$ $$\Gamma_0(N)$$-optimal
25392.be6 25392g5 $$[0, 1, 0, 8288, -2123308]$$ $$207646/6561$$ $$-1989147581908992$$ $$[2]$$ $$90112$$ $$1.6155$$

## Rank

sage: E.rank()

The elliptic curves in class 25392.be have rank $$1$$.

## Complex multiplication

The elliptic curves in class 25392.be do not have complex multiplication.

## Modular form 25392.2.a.be

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.