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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 29575.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29575.h1 | 29575c4 | \([1, -1, 1, -1676005, -794594628]\) | \(6903498885921/374712065\) | \(28260368246102890625\) | \([2]\) | \(516096\) | \(2.4883\) | |
| 29575.h2 | 29575c2 | \([1, -1, 1, -302880, 48504122]\) | \(40743095121/10144225\) | \(765066195750390625\) | \([2, 2]\) | \(258048\) | \(2.1418\) | |
| 29575.h3 | 29575c1 | \([1, -1, 1, -281755, 57630122]\) | \(32798729601/3185\) | \(240209166640625\) | \([4]\) | \(129024\) | \(1.7952\) | \(\Gamma_0(N)\)-optimal |
| 29575.h4 | 29575c3 | \([1, -1, 1, 732245, 307285372]\) | \(575722725759/874680625\) | \(-65967442388681640625\) | \([2]\) | \(516096\) | \(2.4883\) |
Rank
sage: E.rank()
The elliptic curves in class 29575.h have rank \(1\).
Complex multiplication
The elliptic curves in class 29575.h do not have complex multiplication.Modular form 29575.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
