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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 301530.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
301530.bc1 | 301530bc2 | \([1, 0, 1, -91793, 8670956]\) | \(577801395289/114581400\) | \(16962159411864600\) | \([2]\) | \(3649536\) | \(1.8305\) | |
301530.bc2 | 301530bc1 | \([1, 0, 1, -28313, -1714372]\) | \(16954786009/1258560\) | \(186312048459840\) | \([2]\) | \(1824768\) | \(1.4839\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 301530.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 301530.bc do not have complex multiplication.Modular form 301530.2.a.bc
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.