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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 47190.bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47190.bx1 | 47190ce2 | \([1, 1, 1, -37862415, 26623714965]\) | \(3388383326345613179401/1787816842064922240\) | \(3167226592545375708416640\) | \([2]\) | \(9031680\) | \(3.3928\) | |
47190.bx2 | 47190ce1 | \([1, 1, 1, 8988785, 3254336405]\) | \(45338857965533777399/28814396538470400\) | \(-51046461146089160294400\) | \([2]\) | \(4515840\) | \(3.0462\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 47190.bx have rank \(1\).
Complex multiplication
The elliptic curves in class 47190.bx do not have complex multiplication.Modular form 47190.2.a.bx
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.