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SageMath
E = EllipticCurve("da1")
E.isogeny_class()
Elliptic curves in class 353925.da
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 353925.da1 | 353925da8 | \([1, -1, 0, -3539250567, -81042034943534]\) | \(242970740812818720001/24375\) | \(491867683505859375\) | \([2]\) | \(94371840\) | \(3.7424\) | |
| 353925.da2 | 353925da6 | \([1, -1, 0, -221203692, -1266233927909]\) | \(59319456301170001/594140625\) | \(11989274785455322265625\) | \([2, 2]\) | \(47185920\) | \(3.3958\) | |
| 353925.da3 | 353925da7 | \([1, -1, 0, -215894817, -1329903265784]\) | \(-55150149867714721/5950927734375\) | \(-120084883668422698974609375\) | \([2]\) | \(94371840\) | \(3.7424\) | |
| 353925.da4 | 353925da4 | \([1, -1, 0, -14157567, -18781024784]\) | \(15551989015681/1445900625\) | \(29177099117884072265625\) | \([2, 2]\) | \(23592960\) | \(3.0492\) | |
| 353925.da5 | 353925da2 | \([1, -1, 0, -3131442, 1804750591]\) | \(168288035761/27720225\) | \(559371604390203515625\) | \([2, 2]\) | \(11796480\) | \(2.7027\) | |
| 353925.da6 | 353925da1 | \([1, -1, 0, -2995317, 1996006216]\) | \(147281603041/5265\) | \(106243419637265625\) | \([2]\) | \(5898240\) | \(2.3561\) | \(\Gamma_0(N)\)-optimal |
| 353925.da7 | 353925da3 | \([1, -1, 0, 5716683, 10148532466]\) | \(1023887723039/2798036865\) | \(-56462109175448081015625\) | \([2]\) | \(23592960\) | \(3.0492\) | |
| 353925.da8 | 353925da5 | \([1, -1, 0, 16470558, -88950059159]\) | \(24487529386319/183539412225\) | \(-3703676124026164391015625\) | \([2]\) | \(47185920\) | \(3.3958\) |
Rank
sage: E.rank()
The elliptic curves in class 353925.da have rank \(0\).
Complex multiplication
The elliptic curves in class 353925.da do not have complex multiplication.Modular form 353925.2.a.da
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 16 & 16 & 8 \\ 2 & 1 & 2 & 2 & 4 & 8 & 8 & 4 \\ 4 & 2 & 1 & 4 & 8 & 16 & 16 & 8 \\ 4 & 2 & 4 & 1 & 2 & 4 & 4 & 2 \\ 8 & 4 & 8 & 2 & 1 & 2 & 2 & 4 \\ 16 & 8 & 16 & 4 & 2 & 1 & 4 & 8 \\ 16 & 8 & 16 & 4 & 2 & 4 & 1 & 8 \\ 8 & 4 & 8 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
