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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 187200.bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
187200.bq1 | 187200cv3 | \([0, 0, 0, -1130700, 462706000]\) | \(428320044872/73125\) | \(27293760000000000\) | \([2]\) | \(2359296\) | \(2.1603\) | |
187200.bq2 | 187200cv4 | \([0, 0, 0, -482700, -124706000]\) | \(33324076232/1285245\) | \(479715125760000000\) | \([2]\) | \(2359296\) | \(2.1603\) | |
187200.bq3 | 187200cv2 | \([0, 0, 0, -77700, 5704000]\) | \(1111934656/342225\) | \(15966849600000000\) | \([2, 2]\) | \(1179648\) | \(1.8138\) | |
187200.bq4 | 187200cv1 | \([0, 0, 0, 13425, 601000]\) | \(367061696/426465\) | \(-310892985000000\) | \([2]\) | \(589824\) | \(1.4672\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 187200.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 187200.bq do not have complex multiplication.Modular form 187200.2.a.bq
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.