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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 28224.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28224.b1 | 28224cv2 | \([0, 0, 0, -79212, -8345680]\) | \(838561807/26244\) | \(1720250130235392\) | \([2]\) | \(196608\) | \(1.6985\) | |
28224.b2 | 28224cv1 | \([0, 0, 0, 1428, -442960]\) | \(4913/1296\) | \(-84950623715328\) | \([2]\) | \(98304\) | \(1.3519\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28224.b have rank \(1\).
Complex multiplication
The elliptic curves in class 28224.b do not have complex multiplication.Modular form 28224.2.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.