# Properties

 Label 7350.bd Number of curves $8$ Conductor $7350$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7350.bd1")

sage: E.isogeny_class()

## Elliptic curves in class 7350.bd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7350.bd1 7350w7 [1, 0, 1, -7902501, -5380124102] [2] 663552
7350.bd2 7350w4 [1, 0, 1, -7057251, -7216668602] [2] 221184
7350.bd3 7350w6 [1, 0, 1, -3308751, 2254688398] [2, 2] 331776
7350.bd4 7350w3 [1, 0, 1, -3284251, 2290605398] [2] 165888
7350.bd5 7350w2 [1, 0, 1, -442251, -112158602] [2, 2] 110592
7350.bd6 7350w5 [1, 0, 1, -99251, -281600602] [2] 221184
7350.bd7 7350w1 [1, 0, 1, -50251, 1521398] [2] 55296 $$\Gamma_0(N)$$-optimal
7350.bd8 7350w8 [1, 0, 1, 892999, 7590910898] [2] 663552

## Rank

sage: E.rank()

The elliptic curves in class 7350.bd have rank $$1$$.

## Modular form7350.2.a.bd

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.