# Properties

 Label 55825.t Number of curves $4$ Conductor $55825$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 55825.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55825.t1 55825l4 $$[1, -1, 0, -1333892, 593233641]$$ $$16798320881842096017/2132227789307$$ $$33316059207921875$$ $$[2]$$ $$688128$$ $$2.1922$$
55825.t2 55825l3 $$[1, -1, 0, -529142, -141967109]$$ $$1048626554636928177/48569076788309$$ $$758891824817328125$$ $$[2]$$ $$688128$$ $$2.1922$$
55825.t3 55825l2 $$[1, -1, 0, -90517, 7604016]$$ $$5249244962308257/1448621666569$$ $$22634713540140625$$ $$[2, 2]$$ $$344064$$ $$1.8457$$
55825.t4 55825l1 $$[1, -1, 0, 14608, 770891]$$ $$22062729659823/29354283343$$ $$-458660677234375$$ $$[2]$$ $$172032$$ $$1.4991$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 55825.t have rank $$1$$.

## Complex multiplication

The elliptic curves in class 55825.t do not have complex multiplication.

## Modular form 55825.2.a.t

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} + q^{7} - 3q^{8} - 3q^{9} - q^{11} - 6q^{13} + q^{14} - q^{16} + 2q^{17} - 3q^{18} - 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.