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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 355570.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
355570.w1 | 355570w3 | \([1, 1, 1, -5069295, 4390970405]\) | \(16232905099479601/4052240\) | \(3596377916295440\) | \([2]\) | \(7983360\) | \(2.3605\) | |
355570.w2 | 355570w4 | \([1, 1, 1, -5050075, 4425943117]\) | \(-16048965315233521/256572640900\) | \(-227709163242641152900\) | \([2]\) | \(15966720\) | \(2.7071\) | |
355570.w3 | 355570w1 | \([1, 1, 1, -72095, 4043845]\) | \(46694890801/18944000\) | \(16812869732864000\) | \([2]\) | \(2661120\) | \(1.8112\) | \(\Gamma_0(N)\)-optimal |
355570.w4 | 355570w2 | \([1, 1, 1, 235425, 29752517]\) | \(1625964918479/1369000000\) | \(-1214992539289000000\) | \([2]\) | \(5322240\) | \(2.1578\) |
Rank
sage: E.rank()
The elliptic curves in class 355570.w have rank \(0\).
Complex multiplication
The elliptic curves in class 355570.w do not have complex multiplication.Modular form 355570.2.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.