Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 440818.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
440818.o1 | 440818o3 | \([1, 0, 0, -402570647352, -98313106857612224]\) | \(-2812157792529125619433313717497/39177215279104\) | \(-100518015872675438657536\) | \([]\) | \(2281758336\) | \(4.8998\) | |
440818.o2 | 440818o2 | \([1, 0, 0, -4967137937, -135024131935319]\) | \(-5282409060555942439635337/12733300881458665984\) | \(-32670166345301477757058771456\) | \([]\) | \(760586112\) | \(4.3505\) | |
440818.o3 | 440818o1 | \([1, 0, 0, 113132078, -933569647764]\) | \(62412367968676722023/182867427413015464\) | \(-469187787859464326310188776\) | \([]\) | \(253528704\) | \(3.8012\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 440818.o have rank \(1\).
Complex multiplication
The elliptic curves in class 440818.o do not have complex multiplication.Modular form 440818.2.a.o
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 LMFDB numbering.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.