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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 46410.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46410.a1 | 46410b4 | \([1, 1, 0, -41093, -2836347]\) | \(7674388308884766169/1007648705929320\) | \(1007648705929320\) | \([2]\) | \(294912\) | \(1.6070\) | |
46410.a2 | 46410b2 | \([1, 1, 0, -10493, 364413]\) | \(127787213284071769/15197834433600\) | \(15197834433600\) | \([2, 2]\) | \(147456\) | \(1.2604\) | |
46410.a3 | 46410b1 | \([1, 1, 0, -10173, 390717]\) | \(116449478628435289/1996001280\) | \(1996001280\) | \([2]\) | \(73728\) | \(0.91385\) | \(\Gamma_0(N)\)-optimal |
46410.a4 | 46410b3 | \([1, 1, 0, 14987, 1888117]\) | \(372239584720800551/1745320379985000\) | \(-1745320379985000\) | \([2]\) | \(294912\) | \(1.6070\) |
Rank
sage: E.rank()
The elliptic curves in class 46410.a have rank \(2\).
Complex multiplication
The elliptic curves in class 46410.a do not have complex multiplication.Modular form 46410.2.a.a
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.