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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 173417.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 173417.b1 | 173417b4 | \([1, -1, 0, -925103, -342247216]\) | \(82483294977/17\) | \(18045842560217\) | \([2]\) | \(1030400\) | \(1.9309\) | |
| 173417.b2 | 173417b2 | \([1, -1, 0, -58018, -5297985]\) | \(20346417/289\) | \(306779323523689\) | \([2, 2]\) | \(515200\) | \(1.5844\) | |
| 173417.b3 | 173417b3 | \([1, -1, 0, -7013, -14325870]\) | \(-35937/83521\) | \(-88659224498346121\) | \([2]\) | \(1030400\) | \(1.9309\) | |
| 173417.b4 | 173417b1 | \([1, -1, 0, -7013, 98344]\) | \(35937/17\) | \(18045842560217\) | \([2]\) | \(257600\) | \(1.2378\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 173417.b have rank \(0\).
Complex multiplication
The elliptic curves in class 173417.b do not have complex multiplication.Modular form 173417.2.a.b
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.
