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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 213444.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
213444.bb1 | 213444w2 | \([0, 0, 0, -37191, 2075150]\) | \(194672/49\) | \(1431956645247744\) | \([2]\) | \(995328\) | \(1.6180\) | |
213444.bb2 | 213444w1 | \([0, 0, 0, -12936, -539539]\) | \(131072/7\) | \(12785327189712\) | \([2]\) | \(497664\) | \(1.2715\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 213444.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 213444.bb do not have complex multiplication.Modular form 213444.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.