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SageMath
sage: E = EllipticCurve("b1")
sage: E.isogeny_class()
Elliptic curves in class 168.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 168.b1 | 168a3 | \([0, 1, 0, -152, 672]\) | \(381775972/567\) | \(580608\) | \([4]\) | \(32\) | \(0.0069590\) | |
| 168.b2 | 168a2 | \([0, 1, 0, -12, 0]\) | \(810448/441\) | \(112896\) | \([2, 2]\) | \(16\) | \(-0.33961\) | |
| 168.b3 | 168a1 | \([0, 1, 0, -7, -10]\) | \(2725888/21\) | \(336\) | \([2]\) | \(8\) | \(-0.68619\) | \(\Gamma_0(N)\)-optimal |
| 168.b4 | 168a4 | \([0, 1, 0, 48, 48]\) | \(11696828/7203\) | \(-7375872\) | \([2]\) | \(32\) | \(0.0069590\) |
Rank
sage: E.rank()
The elliptic curves in class 168.b have rank \(0\).
Complex multiplication
The elliptic curves in class 168.b do not have complex multiplication.Modular form 168.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
