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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 48400.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
48400.w1 | 48400cp4 | \([0, 1, 0, -21478508, -38320869512]\) | \(154639330142416/33275\) | \(235794769100000000\) | \([2]\) | \(2488320\) | \(2.7181\) | |
48400.w2 | 48400cp3 | \([0, 1, 0, -1347133, -594672762]\) | \(610462990336/8857805\) | \(3923035470901250000\) | \([2]\) | \(1244160\) | \(2.3715\) | |
48400.w3 | 48400cp2 | \([0, 1, 0, -303508, -36469512]\) | \(436334416/171875\) | \(1217948187500000000\) | \([2]\) | \(829440\) | \(2.1688\) | |
48400.w4 | 48400cp1 | \([0, 1, 0, -137133, 19099738]\) | \(643956736/15125\) | \(6698715031250000\) | \([2]\) | \(414720\) | \(1.8222\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 48400.w have rank \(1\).
Complex multiplication
The elliptic curves in class 48400.w do not have complex multiplication.Modular form 48400.2.a.w
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.