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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 296208bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
296208.bb2 | 296208bb1 | \([0, 0, 0, -209451, -29902246]\) | \(192100033/38148\) | \(201797304653463552\) | \([2]\) | \(2211840\) | \(2.0368\) | \(\Gamma_0(N)\)-optimal |
296208.bb1 | 296208bb2 | \([0, 0, 0, -3171531, -2173855750]\) | \(666940371553/37026\) | \(195862089810714624\) | \([2]\) | \(4423680\) | \(2.3834\) |
Rank
sage: E.rank()
The elliptic curves in class 296208bb have rank \(1\).
Complex multiplication
The elliptic curves in class 296208bb do not have complex multiplication.Modular form 296208.2.a.bb
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.