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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 4730.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4730.b1 | 4730a2 | \([1, -1, 0, -230, 1400]\) | \(1348866350649/2033900\) | \(2033900\) | \([2]\) | \(1152\) | \(0.11073\) | |
4730.b2 | 4730a1 | \([1, -1, 0, -10, 36]\) | \(-116930169/416240\) | \(-416240\) | \([2]\) | \(576\) | \(-0.23584\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4730.b have rank \(1\).
Complex multiplication
The elliptic curves in class 4730.b do not have complex multiplication.Modular form 4730.2.a.b
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.