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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 2310.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2310.f1 | 2310f4 | \([1, 0, 1, -26044, 1615406]\) | \(1953542217204454969/170843779260\) | \(170843779260\) | \([2]\) | \(5120\) | \(1.1966\) | |
| 2310.f2 | 2310f3 | \([1, 0, 1, -9444, -335954]\) | \(93137706732176569/5369647977540\) | \(5369647977540\) | \([2]\) | \(5120\) | \(1.1966\) | |
| 2310.f3 | 2310f2 | \([1, 0, 1, -1744, 21326]\) | \(586145095611769/140040608400\) | \(140040608400\) | \([2, 2]\) | \(2560\) | \(0.85005\) | |
| 2310.f4 | 2310f1 | \([1, 0, 1, 256, 2126]\) | \(1865864036231/2993760000\) | \(-2993760000\) | \([2]\) | \(1280\) | \(0.50348\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2310.f have rank \(1\).
Complex multiplication
The elliptic curves in class 2310.f do not have complex multiplication.Modular form 2310.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
