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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 7350.cj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7350.cj1 | 7350cq2 | \([1, 0, 0, -168463, -25898083]\) | \(838561807/26244\) | \(16547500970437500\) | \([2]\) | \(71680\) | \(1.8872\) | |
7350.cj2 | 7350cq1 | \([1, 0, 0, 3037, -1373583]\) | \(4913/1296\) | \(-817160541750000\) | \([2]\) | \(35840\) | \(1.5406\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7350.cj have rank \(0\).
Complex multiplication
The elliptic curves in class 7350.cj do not have complex multiplication.Modular form 7350.2.a.cj
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.