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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 176b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176.b3 | 176b1 | \([0, 1, 0, -5, -13]\) | \(-4096/11\) | \(-45056\) | \([]\) | \(8\) | \(-0.41958\) | \(\Gamma_0(N)\)-optimal |
| 176.b2 | 176b2 | \([0, 1, 0, -165, 1427]\) | \(-122023936/161051\) | \(-659664896\) | \([]\) | \(40\) | \(0.38514\) | |
| 176.b1 | 176b3 | \([0, 1, 0, -125125, 16994227]\) | \(-52893159101157376/11\) | \(-45056\) | \([]\) | \(200\) | \(1.1899\) |
Rank
sage: E.rank()
The elliptic curves in class 176b have rank \(0\).
Complex multiplication
The elliptic curves in class 176b do not have complex multiplication.Modular form 176.2.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.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
