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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 23100bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23100.bh2 | 23100bc1 | \([0, 1, 0, -533, 14688]\) | \(-67108864/343035\) | \(-85758750000\) | \([2]\) | \(23040\) | \(0.78222\) | \(\Gamma_0(N)\)-optimal |
23100.bh1 | 23100bc2 | \([0, 1, 0, -12908, 559188]\) | \(59466754384/121275\) | \(485100000000\) | \([2]\) | \(46080\) | \(1.1288\) |
Rank
sage: E.rank()
The elliptic curves in class 23100bc have rank \(1\).
Complex multiplication
The elliptic curves in class 23100bc do not have complex multiplication.Modular form 23100.2.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 Cremona 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 Cremona labels.