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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 261392.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 261392.d1 | 261392d4 | \([0, 0, 0, -1394411, -633773734]\) | \(82483294977/17\) | \(61798656315392\) | \([2]\) | \(1935360\) | \(2.0335\) | |
| 261392.d2 | 261392d2 | \([0, 0, 0, -87451, -9831030]\) | \(20346417/289\) | \(1050577157361664\) | \([2, 2]\) | \(967680\) | \(1.6869\) | |
| 261392.d3 | 261392d3 | \([0, 0, 0, -10571, -26513990]\) | \(-35937/83521\) | \(-303616798477520896\) | \([2]\) | \(1935360\) | \(2.0335\) | |
| 261392.d4 | 261392d1 | \([0, 0, 0, -10571, 178746]\) | \(35937/17\) | \(61798656315392\) | \([2]\) | \(483840\) | \(1.3404\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 261392.d have rank \(1\).
Complex multiplication
The elliptic curves in class 261392.d do not have complex multiplication.Modular form 261392.2.a.d
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.
