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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 3696.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3696.bb1 | 3696z3 | \([0, 1, 0, -1472072, -687941772]\) | \(86129359107301290313/9166294368\) | \(37545141731328\) | \([2]\) | \(46080\) | \(2.0325\) | |
3696.bb2 | 3696z2 | \([0, 1, 0, -92232, -10716300]\) | \(21184262604460873/216872764416\) | \(888310843047936\) | \([2, 2]\) | \(23040\) | \(1.6859\) | |
3696.bb3 | 3696z4 | \([0, 1, 0, -23112, -26337420]\) | \(-333345918055753/72923718045024\) | \(-298695549112418304\) | \([2]\) | \(46080\) | \(2.0325\) | |
3696.bb4 | 3696z1 | \([0, 1, 0, -10312, 129908]\) | \(29609739866953/15259926528\) | \(62504659058688\) | \([2]\) | \(11520\) | \(1.3393\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3696.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 3696.bb do not have complex multiplication.Modular form 3696.2.a.bb
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.