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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 3150.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3150.bj1 | 3150bm4 | \([1, -1, 1, -60230, 5704147]\) | \(2121328796049/120050\) | \(1367444531250\) | \([2]\) | \(12288\) | \(1.3930\) | |
3150.bj2 | 3150bm3 | \([1, -1, 1, -19730, -991853]\) | \(74565301329/5468750\) | \(62292480468750\) | \([2]\) | \(12288\) | \(1.3930\) | |
3150.bj3 | 3150bm2 | \([1, -1, 1, -3980, 79147]\) | \(611960049/122500\) | \(1395351562500\) | \([2, 2]\) | \(6144\) | \(1.0464\) | |
3150.bj4 | 3150bm1 | \([1, -1, 1, 520, 7147]\) | \(1367631/2800\) | \(-31893750000\) | \([2]\) | \(3072\) | \(0.69987\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3150.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 3150.bj do not have complex multiplication.Modular form 3150.2.a.bj
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.