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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 6050h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6050.i1 | 6050h1 | \([1, 1, 0, -267775, -53954875]\) | \(-76711450249/851840\) | \(-23579476910000000\) | \([]\) | \(80640\) | \(1.9565\) | \(\Gamma_0(N)\)-optimal |
| 6050.i2 | 6050h2 | \([1, 1, 0, 896850, -278727500]\) | \(2882081488391/2883584000\) | \(-79819452416000000000\) | \([]\) | \(241920\) | \(2.5058\) |
Rank
sage: E.rank()
The elliptic curves in class 6050h have rank \(0\).
Complex multiplication
The elliptic curves in class 6050h do not have complex multiplication.Modular form 6050.2.a.h
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
