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SageMath
E = EllipticCurve("qz1")
E.isogeny_class()
Elliptic curves in class 302400qz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 302400.qz3 | 302400qz1 | \([0, 0, 0, 16500, -502000]\) | \(4492125/3584\) | \(-396361728000000\) | \([]\) | \(995328\) | \(1.4890\) | \(\Gamma_0(N)\)-optimal |
| 302400.qz2 | 302400qz2 | \([0, 0, 0, -175500, 36234000]\) | \(-7414875/2744\) | \(-221225582592000000\) | \([]\) | \(2985984\) | \(2.0383\) | |
| 302400.qz1 | 302400qz3 | \([0, 0, 0, -15295500, 23024682000]\) | \(-545407363875/14\) | \(-10158317568000000\) | \([]\) | \(8957952\) | \(2.5876\) |
Rank
sage: E.rank()
The elliptic curves in class 302400qz have rank \(1\).
Complex multiplication
The elliptic curves in class 302400qz do not have complex multiplication.Modular form 302400.2.a.qz
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.
