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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 19890l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19890.m4 | 19890l1 | \([1, -1, 0, 14220, -114224]\) | \(436192097814719/259683840000\) | \(-189309519360000\) | \([2]\) | \(92160\) | \(1.4289\) | \(\Gamma_0(N)\)-optimal |
19890.m3 | 19890l2 | \([1, -1, 0, -57780, -877424]\) | \(29263955267177281/16463793153600\) | \(12002105208974400\) | \([2, 2]\) | \(184320\) | \(1.7754\) | |
19890.m1 | 19890l3 | \([1, -1, 0, -689580, -219859304]\) | \(49745123032831462081/97939634471640\) | \(71397993529825560\) | \([2]\) | \(368640\) | \(2.1220\) | |
19890.m2 | 19890l4 | \([1, -1, 0, -577980, 168395656]\) | \(29291056630578924481/175463302795560\) | \(127912747737963240\) | \([2]\) | \(368640\) | \(2.1220\) |
Rank
sage: E.rank()
The elliptic curves in class 19890l have rank \(0\).
Complex multiplication
The elliptic curves in class 19890l do not have complex multiplication.Modular form 19890.2.a.l
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.