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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 50784.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 50784.p1 | 50784q4 | \([0, 1, 0, -17104, -866404]\) | \(7301384/3\) | \(227383125504\) | \([2]\) | \(101376\) | \(1.1415\) | |
| 50784.p2 | 50784q3 | \([0, 1, 0, -9169, 328607]\) | \(140608/3\) | \(1819065004032\) | \([2]\) | \(101376\) | \(1.1415\) | |
| 50784.p3 | 50784q1 | \([0, 1, 0, -1234, -9424]\) | \(21952/9\) | \(85268672064\) | \([2, 2]\) | \(50688\) | \(0.79495\) | \(\Gamma_0(N)\)-optimal |
| 50784.p4 | 50784q2 | \([0, 1, 0, 4056, -64440]\) | \(97336/81\) | \(-6139344388608\) | \([2]\) | \(101376\) | \(1.1415\) |
Rank
sage: E.rank()
The elliptic curves in class 50784.p have rank \(1\).
Complex multiplication
The elliptic curves in class 50784.p do not have complex multiplication.Modular form 50784.2.a.p
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
