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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 28050.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28050.v1 | 28050k4 | \([1, 1, 0, -2112150, 1180624500]\) | \(66692696957462376289/1322972640\) | \(20671447500000\) | \([2]\) | \(491520\) | \(2.0874\) | |
| 28050.v2 | 28050k3 | \([1, 1, 0, -200150, -2647500]\) | \(56751044592329569/32660264340000\) | \(510316630312500000\) | \([2]\) | \(491520\) | \(2.0874\) | |
| 28050.v3 | 28050k2 | \([1, 1, 0, -132150, 18364500]\) | \(16334668434139489/72511718400\) | \(1132995600000000\) | \([2, 2]\) | \(245760\) | \(1.7408\) | |
| 28050.v4 | 28050k1 | \([1, 1, 0, -4150, 572500]\) | \(-506071034209/8823767040\) | \(-137871360000000\) | \([2]\) | \(122880\) | \(1.3943\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28050.v have rank \(0\).
Complex multiplication
The elliptic curves in class 28050.v do not have complex multiplication.Modular form 28050.2.a.v
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.
