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SageMath
E = EllipticCurve("er1")
E.isogeny_class()
Elliptic curves in class 154560.er
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154560.er1 | 154560bz3 | \([0, 1, 0, -184801, 9994655]\) | \(2662558086295801/1374177967680\) | \(360232509159505920\) | \([2]\) | \(1658880\) | \(2.0609\) | |
| 154560.er2 | 154560bz1 | \([0, 1, 0, -103201, -12794785]\) | \(463702796512201/15214500\) | \(3988389888000\) | \([2]\) | \(552960\) | \(1.5116\) | \(\Gamma_0(N)\)-optimal |
| 154560.er3 | 154560bz2 | \([0, 1, 0, -98721, -13951521]\) | \(-405897921250921/84358968750\) | \(-22114197504000000\) | \([2]\) | \(1105920\) | \(1.8581\) | |
| 154560.er4 | 154560bz4 | \([0, 1, 0, 693279, 78309279]\) | \(140574743422291079/91397357868600\) | \(-23959268981106278400\) | \([2]\) | \(3317760\) | \(2.4075\) |
Rank
sage: E.rank()
The elliptic curves in class 154560.er have rank \(0\).
Complex multiplication
The elliptic curves in class 154560.er do not have complex multiplication.Modular form 154560.2.a.er
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.
