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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 161700.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
161700.bh1 | 161700ej2 | \([0, -1, 0, -2229908, -1233767688]\) | \(2605772594896/108945375\) | \(51269257693500000000\) | \([2]\) | \(3981312\) | \(2.5468\) | |
161700.bh2 | 161700ej1 | \([0, -1, 0, 66967, -71548938]\) | \(1129201664/75796875\) | \(-2229356636718750000\) | \([2]\) | \(1990656\) | \(2.2003\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 161700.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 161700.bh do not have complex multiplication.Modular form 161700.2.a.bh
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.