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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 441525.bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
441525.bz1 | 441525bz1 | \([1, 1, 0, -15155, 688800]\) | \(5177717/189\) | \(14052700958625\) | \([2]\) | \(1204224\) | \(1.2924\) | \(\Gamma_0(N)\)-optimal |
441525.bz2 | 441525bz2 | \([1, 1, 0, 5870, 2475925]\) | \(300763/35721\) | \(-2655960481180125\) | \([2]\) | \(2408448\) | \(1.6390\) |
Rank
sage: E.rank()
The elliptic curves in class 441525.bz have rank \(0\).
Complex multiplication
The elliptic curves in class 441525.bz do not have complex multiplication.Modular form 441525.2.a.bz
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.