# Properties

 Label 25200.ev Number of curves 4 Conductor 25200 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("25200.ev1")

sage: E.isogeny_class()

## Elliptic curves in class 25200.ev

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25200.ev1 25200ei4 [0, 0, 0, -405075, -99224750] [2] 196608
25200.ev2 25200ei2 [0, 0, 0, -27075, -1322750] [2, 2] 98304
25200.ev3 25200ei1 [0, 0, 0, -9075, 315250] [2] 49152 $$\Gamma_0(N)$$-optimal
25200.ev4 25200ei3 [0, 0, 0, 62925, -8252750] [2] 196608

## Rank

sage: E.rank()

The elliptic curves in class 25200.ev have rank $$0$$.

## Modular form 25200.2.a.ev

sage: E.q_eigenform(10)

$$q + q^{7} + 6q^{13} + 2q^{17} + 8q^{19} + O(q^{20})$$

## 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.