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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 369600i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.i3 | 369600i1 | \([0, -1, 0, -58697233, -173071463663]\) | \(87364831012240243408/1760913\) | \(450793728000000\) | \([2]\) | \(23592960\) | \(2.7953\) | \(\Gamma_0(N)\)-optimal |
| 369600.i2 | 369600i2 | \([0, -1, 0, -58699233, -173059077663]\) | \(21843440425782779332/3100814593569\) | \(3175234143814656000000\) | \([2, 2]\) | \(47185920\) | \(3.1419\) | |
| 369600.i1 | 369600i3 | \([0, -1, 0, -64023233, -139789401663]\) | \(14171198121996897746/4077720290568771\) | \(8351171155084843008000000\) | \([2]\) | \(94371840\) | \(3.4884\) | |
| 369600.i4 | 369600i4 | \([0, -1, 0, -53407233, -205536081663]\) | \(-8226100326647904626/4152140742401883\) | \(-8503584240439056384000000\) | \([2]\) | \(94371840\) | \(3.4884\) |
Rank
sage: E.rank()
The elliptic curves in class 369600i have rank \(1\).
Complex multiplication
The elliptic curves in class 369600i do not have complex multiplication.Modular form 369600.2.a.i
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 Cremona 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 Cremona labels.
