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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 4950.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4950.d1 | 4950b4 | \([1, -1, 0, -33117, 588041]\) | \(13060888875/7086244\) | \(2179352197687500\) | \([2]\) | \(27648\) | \(1.6341\) | |
| 4950.d2 | 4950b2 | \([1, -1, 0, -25617, 1584541]\) | \(4406910829875/7744\) | \(3267000000\) | \([2]\) | \(9216\) | \(1.0848\) | |
| 4950.d3 | 4950b3 | \([1, -1, 0, -19617, -1045459]\) | \(2714704875/21296\) | \(6549518250000\) | \([2]\) | \(13824\) | \(1.2875\) | |
| 4950.d4 | 4950b1 | \([1, -1, 0, -1617, 24541]\) | \(1108717875/45056\) | \(19008000000\) | \([2]\) | \(4608\) | \(0.73820\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4950.d have rank \(1\).
Complex multiplication
The elliptic curves in class 4950.d do not have complex multiplication.Modular form 4950.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
