# Properties

 Label 7605q Number of curves 8 Conductor 7605 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7605.g1")

sage: E.isogeny_class()

## Elliptic curves in class 7605q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7605.g7 7605q1 [1, -1, 1, -32, -11046] [2] 4608 $$\Gamma_0(N)$$-optimal
7605.g6 7605q2 [1, -1, 1, -7637, -251364] [2, 2] 9216
7605.g4 7605q3 [1, -1, 1, -121712, -16313124] [2] 18432
7605.g5 7605q4 [1, -1, 1, -15242, 338784] [2, 2] 18432
7605.g2 7605q5 [1, -1, 1, -205367, 35854134] [2, 2] 36864
7605.g8 7605q6 [1, -1, 1, 53203, 2501646] [2] 36864
7605.g1 7605q7 [1, -1, 1, -3285392, 2292896454] [2] 73728
7605.g3 7605q8 [1, -1, 1, -167342, 49512714] [2] 73728

## Rank

sage: E.rank()

The elliptic curves in class 7605q have rank $$1$$.

## Modular form7605.2.a.g

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} + q^{5} + 3q^{8} - q^{10} - 4q^{11} - q^{16} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 8 & 8 & 16 & 16 \\ 4 & 2 & 4 & 1 & 2 & 2 & 4 & 4 \\ 8 & 4 & 8 & 2 & 1 & 4 & 2 & 2 \\ 8 & 4 & 8 & 2 & 4 & 1 & 8 & 8 \\ 16 & 8 & 16 & 4 & 2 & 8 & 1 & 4 \\ 16 & 8 & 16 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.