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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 6422.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6422.b1 | 6422b2 | \([1, 1, 0, -11833, -553405]\) | \(-37966934881/4952198\) | \(-23903313876182\) | \([]\) | \(23400\) | \(1.3003\) | |
6422.b2 | 6422b1 | \([1, 1, 0, -3, 2605]\) | \(-1/608\) | \(-2934699872\) | \([]\) | \(4680\) | \(0.49554\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6422.b have rank \(0\).
Complex multiplication
The elliptic curves in class 6422.b do not have complex multiplication.Modular form 6422.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.