Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 9450.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9450.u1 | 9450bd2 | \([1, -1, 0, -49487667, -133984168759]\) | \(-43581616978927713867/6860\) | \(-2109771562500\) | \([]\) | \(466560\) | \(2.6811\) | |
| 9450.u2 | 9450bd1 | \([1, -1, 0, -610167, -184156259]\) | \(-59550644977653843/322828856000\) | \(-136193423625000000\) | \([]\) | \(155520\) | \(2.1317\) | \(\Gamma_0(N)\)-optimal |
| 9450.u3 | 9450bd3 | \([1, -1, 0, 1576458, -981759884]\) | \(114115456478544693/175616000000000\) | \(-666792000000000000000\) | \([]\) | \(466560\) | \(2.6811\) |
Rank
sage: E.rank()
The elliptic curves in class 9450.u have rank \(0\).
Complex multiplication
The elliptic curves in class 9450.u do not have complex multiplication.Modular form 9450.2.a.u
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.
