# Properties

 Label 63525.t Number of curves $6$ Conductor $63525$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("63525.t1")

sage: E.isogeny_class()

## Elliptic curves in class 63525.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
63525.t1 63525bj6 [1, 0, 0, -40081313, 97661942742] [2] 5898240
63525.t2 63525bj4 [1, 0, 0, -2646938, 1343295867] [2, 2] 2949120
63525.t3 63525bj2 [1, 0, 0, -816813, -265384008] [2, 2] 1474560
63525.t4 63525bj1 [1, 0, 0, -801688, -276349633] [2] 737280 $$\Gamma_0(N)$$-optimal
63525.t5 63525bj3 [1, 0, 0, 771312, -1172203383] [2] 2949120
63525.t6 63525bj5 [1, 0, 0, 5505437, 7987481492] [2] 5898240

## Rank

sage: E.rank()

The elliptic curves in class 63525.t have rank $$1$$.

## Modular form 63525.2.a.t

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} - q^{4} - q^{6} - q^{7} + 3q^{8} + q^{9} - q^{12} - 2q^{13} + q^{14} - q^{16} - 6q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.