Properties

 Label 14400m Number of curves 2 Conductor 14400 CM -3 Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("14400.c1")

sage: E.isogeny_class()

Elliptic curves in class 14400m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.c2 14400m1 [0, 0, 0, 0, 10] [] 1152 $$\Gamma_0(N)$$-optimal
14400.c1 14400m2 [0, 0, 0, 0, -270] [] 3456

Rank

sage: E.rank()

The elliptic curves in class 14400m have rank $$1$$.

Modular form 14400.2.a.c

sage: E.q_eigenform(10)

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

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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.