# Properties

 Label 25200eq Number of curves $3$ Conductor $25200$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("eq1")

sage: E.isogeny_class()

## Elliptic curves in class 25200eq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25200.dn2 25200eq1 $$[0, 0, 0, -4800, 142000]$$ $$-262144/35$$ $$-1632960000000$$ $$[]$$ $$34560$$ $$1.0760$$ $$\Gamma_0(N)$$-optimal
25200.dn3 25200eq2 $$[0, 0, 0, 31200, -362000]$$ $$71991296/42875$$ $$-2000376000000000$$ $$[]$$ $$103680$$ $$1.6253$$
25200.dn1 25200eq3 $$[0, 0, 0, -472800, -130898000]$$ $$-250523582464/13671875$$ $$-637875000000000000$$ $$[]$$ $$311040$$ $$2.1746$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 25200eq do not have complex multiplication.

## Modular form 25200.2.a.eq

sage: E.q_eigenform(10)

$$q + q^{7} - 3q^{11} - 5q^{13} + 3q^{17} - 2q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 