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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 126126.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 126126.bb1 | 126126ce1 | \([1, -1, 0, -2546510850, 49514613663892]\) | \(-21293376668673906679951249/26211168887701209984\) | \(-2248030282374017387334152064\) | \([]\) | \(106686720\) | \(4.1581\) | \(\Gamma_0(N)\)-optimal |
| 126126.bb2 | 126126ce2 | \([1, -1, 0, 7211712240, -3107478259714298]\) | \(483641001192506212470106511/48918776756543177755473774\) | \(-4195573726473669725100472113210654\) | \([]\) | \(746807040\) | \(5.1310\) |
Rank
sage: E.rank()
The elliptic curves in class 126126.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 126126.bb do not have complex multiplication.Modular form 126126.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
