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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 348480.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 348480.h1 | 348480h3 | \([0, 0, 0, -109261548, 93114779472]\) | \(15781142246787/8722841600\) | \(79734323066080901411635200\) | \([2]\) | \(119439360\) | \(3.6606\) | |
| 348480.h2 | 348480h1 | \([0, 0, 0, -83125548, 291708497872]\) | \(5066026756449723/11000000\) | \(137928013774848000000\) | \([2]\) | \(39813120\) | \(3.1113\) | \(\Gamma_0(N)\)-optimal |
| 348480.h3 | 348480h2 | \([0, 0, 0, -82196268, 298549113808]\) | \(-4898016158612283/236328125000\) | \(-2963297170944000000000000\) | \([2]\) | \(79626240\) | \(3.4578\) | |
| 348480.h4 | 348480h4 | \([0, 0, 0, 426003732, 736075433808]\) | \(935355271080573/566899520000\) | \(-5181952343796566395453440000\) | \([2]\) | \(238878720\) | \(4.0071\) |
Rank
sage: E.rank()
The elliptic curves in class 348480.h have rank \(1\).
Complex multiplication
The elliptic curves in class 348480.h do not have complex multiplication.Modular form 348480.2.a.h
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
