# Properties

 Label 5880bf Number of curves $6$ Conductor $5880$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("5880.t1")

sage: E.isogeny_class()

## Elliptic curves in class 5880bf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5880.t4 5880bf1 [0, 1, 0, -8591, -309366]  6144 $$\Gamma_0(N)$$-optimal
5880.t3 5880bf2 [0, 1, 0, -8836, -291040] [2, 2] 12288
5880.t2 5880bf3 [0, 1, 0, -33336, 2021760] [2, 2] 24576
5880.t5 5880bf4 [0, 1, 0, 11744, -1427056]  24576
5880.t1 5880bf5 [0, 1, 0, -513536, 141471840]  49152
5880.t6 5880bf6 [0, 1, 0, 54864, 10982880]  49152

## Rank

sage: E.rank()

The elliptic curves in class 5880bf have rank $$0$$.

## Modular form5880.2.a.t

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{9} - 4q^{11} + 2q^{13} - q^{15} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 