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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 44352.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44352.b1 | 44352bc2 | \([0, 0, 0, -2037612, 1119473840]\) | \(9791533777258802/427901859\) | \(40886659345416192\) | \([2]\) | \(983040\) | \(2.2657\) | |
44352.b2 | 44352bc1 | \([0, 0, 0, -120972, 19322480]\) | \(-4097989445764/1004475087\) | \(-47989544610889728\) | \([2]\) | \(491520\) | \(1.9191\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 44352.b have rank \(0\).
Complex multiplication
The elliptic curves in class 44352.b do not have complex multiplication.Modular form 44352.2.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.