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SageMath
E = EllipticCurve("fh1")
E.isogeny_class()
Elliptic curves in class 97344fh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97344.br3 | 97344fh1 | \([0, 0, 0, -44616, 2091544]\) | \(2725888/1053\) | \(3794162872660992\) | \([2]\) | \(344064\) | \(1.6883\) | \(\Gamma_0(N)\)-optimal |
| 97344.br2 | 97344fh2 | \([0, 0, 0, -318396, -67667600]\) | \(61918288/1521\) | \(87687319723720704\) | \([2, 2]\) | \(688128\) | \(2.0349\) | |
| 97344.br4 | 97344fh3 | \([0, 0, 0, 46644, -213829616]\) | \(48668/85683\) | \(-19758876044411731968\) | \([2]\) | \(1376256\) | \(2.3815\) | |
| 97344.br1 | 97344fh4 | \([0, 0, 0, -5063916, -4386090800]\) | \(62275269892/39\) | \(8993571253714944\) | \([2]\) | \(1376256\) | \(2.3815\) |
Rank
sage: E.rank()
The elliptic curves in class 97344fh have rank \(1\).
Complex multiplication
The elliptic curves in class 97344fh do not have complex multiplication.Modular form 97344.2.a.fh
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.
