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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 9450b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9450.l3 | 9450b1 | \([1, -1, 0, 258, 916]\) | \(4492125/3584\) | \(-1512000000\) | \([]\) | \(5184\) | \(0.44930\) | \(\Gamma_0(N)\)-optimal |
| 9450.l2 | 9450b2 | \([1, -1, 0, -2742, -70084]\) | \(-7414875/2744\) | \(-843908625000\) | \([]\) | \(15552\) | \(0.99860\) | |
| 9450.l1 | 9450b3 | \([1, -1, 0, -238992, -44910334]\) | \(-545407363875/14\) | \(-38750906250\) | \([]\) | \(46656\) | \(1.5479\) |
Rank
sage: E.rank()
The elliptic curves in class 9450b have rank \(1\).
Complex multiplication
The elliptic curves in class 9450b do not have complex multiplication.Modular form 9450.2.a.b
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
