# Properties

 Label 17424.t Number of curves $2$ Conductor $17424$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 17424.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17424.t1 17424bt2 [0, 0, 0, -523083, 145619386] [] 101376
17424.t2 17424bt1 [0, 0, 0, -363, -10406] [] 9216 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 17424.t have rank $$0$$.

## Complex multiplication

The elliptic curves in class 17424.t do not have complex multiplication.

## Modular form 17424.2.a.t

sage: E.q_eigenform(10)

$$q - q^{5} + 2q^{7} + q^{13} + 5q^{17} - 6q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 