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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 49098.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
49098.b1 | 49098e2 | \([1, 1, 0, -6101, 180405]\) | \(213525509833/669336\) | \(78746711064\) | \([2]\) | \(82944\) | \(0.95810\) | |
49098.b2 | 49098e1 | \([1, 1, 0, -221, 5181]\) | \(-10218313/96192\) | \(-11316892608\) | \([2]\) | \(41472\) | \(0.61153\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 49098.b have rank \(2\).
Complex multiplication
The elliptic curves in class 49098.b do not have complex multiplication.Modular form 49098.2.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.