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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 48050.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48050.f1 | 48050l2 | \([1, 1, 0, -120625, 16075325]\) | \(-349938025/8\) | \(-4437518405000\) | \([]\) | \(183600\) | \(1.5402\) | |
| 48050.f2 | 48050l3 | \([1, 1, 0, -72575, -9102875]\) | \(-121945/32\) | \(-11093796012500000\) | \([]\) | \(306000\) | \(1.7956\) | |
| 48050.f3 | 48050l1 | \([1, 1, 0, -500, 50650]\) | \(-25/2\) | \(-1109379601250\) | \([]\) | \(61200\) | \(0.99089\) | \(\Gamma_0(N)\)-optimal |
| 48050.f4 | 48050l4 | \([1, 1, 0, 528050, 67176500]\) | \(46969655/32768\) | \(-11360047116800000000\) | \([]\) | \(918000\) | \(2.3449\) |
Rank
sage: E.rank()
The elliptic curves in class 48050.f have rank \(1\).
Complex multiplication
The elliptic curves in class 48050.f do not have complex multiplication.Modular form 48050.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
