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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 28050.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28050.t1 | 28050h4 | \([1, 1, 0, -4460650, -3158052500]\) | \(628200507126935410849/88124751829125000\) | \(1376949247330078125000\) | \([2]\) | \(1990656\) | \(2.7824\) | |
| 28050.t2 | 28050h2 | \([1, 1, 0, -1139650, 467264500]\) | \(10476561483361670689/13992628953600\) | \(218634827400000000\) | \([2]\) | \(663552\) | \(2.2331\) | |
| 28050.t3 | 28050h1 | \([1, 1, 0, -51650, 11392500]\) | \(-975276594443809/3037581803520\) | \(-47462215680000000\) | \([2]\) | \(331776\) | \(1.8865\) | \(\Gamma_0(N)\)-optimal |
| 28050.t4 | 28050h3 | \([1, 1, 0, 452350, -264295500]\) | \(655127711084516831/2313151512408000\) | \(-36142992381375000000\) | \([2]\) | \(995328\) | \(2.4358\) |
Rank
sage: E.rank()
The elliptic curves in class 28050.t have rank \(0\).
Complex multiplication
The elliptic curves in class 28050.t do not have complex multiplication.Modular form 28050.2.a.t
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
