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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 43190b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43190.a2 | 43190b1 | \([1, 0, 1, 3146, -26448]\) | \(3445071928362791/2301874107400\) | \(-2301874107400\) | \([3]\) | \(67392\) | \(1.0608\) | \(\Gamma_0(N)\)-optimal |
43190.a1 | 43190b2 | \([1, 0, 1, -55469, -5164824]\) | \(-18873978957685236169/580715464000000\) | \(-580715464000000\) | \([]\) | \(202176\) | \(1.6101\) |
Rank
sage: E.rank()
The elliptic curves in class 43190b have rank \(1\).
Complex multiplication
The elliptic curves in class 43190b do not have complex multiplication.Modular form 43190.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.