# Properties

 Label 248430cb Number of curves 8 Conductor 248430 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("248430.cb1")

sage: E.isogeny_class()

## Elliptic curves in class 248430cb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
248430.cb7 248430cb1 [1, 1, 0, -213028897, -1190430079691] [2] 74317824 $$\Gamma_0(N)$$-optimal
248430.cb6 248430cb2 [1, 1, 0, -342874977, 432048628341] [2, 2] 148635648
248430.cb5 248430cb3 [1, 1, 0, -1316058097, 17575334152069] [2] 222953472
248430.cb4 248430cb4 [1, 1, 0, -4110729977, 101275673419341] [2] 297271296
248430.cb8 248430cb5 [1, 1, 0, 1347442743, 3429658072989] [2] 297271296
248430.cb2 248430cb6 [1, 1, 0, -20801085477, 1154709841032441] [2, 2] 445906944
248430.cb1 248430cb7 [1, 1, 0, -332817158027, 73901943591424551] [2] 891813888
248430.cb3 248430cb8 [1, 1, 0, -20545451007, 1184474231531739] [2] 891813888

## Rank

sage: E.rank()

The elliptic curves in class 248430cb have rank $$1$$.

## Modular form 248430.2.a.cb

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} + q^{9} - q^{10} - q^{12} - q^{15} + q^{16} - 6q^{17} - q^{18} - 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.