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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 5850.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5850.m1 | 5850n3 | \([1, -1, 0, -108792, 13836366]\) | \(12501706118329/2570490\) | \(29279487656250\) | \([2]\) | \(24576\) | \(1.5811\) | |
| 5850.m2 | 5850n2 | \([1, -1, 0, -7542, 167616]\) | \(4165509529/1368900\) | \(15592626562500\) | \([2, 2]\) | \(12288\) | \(1.2345\) | |
| 5850.m3 | 5850n1 | \([1, -1, 0, -3042, -61884]\) | \(273359449/9360\) | \(106616250000\) | \([2]\) | \(6144\) | \(0.88791\) | \(\Gamma_0(N)\)-optimal |
| 5850.m4 | 5850n4 | \([1, -1, 0, 21708, 1132866]\) | \(99317171591/106616250\) | \(-1214425722656250\) | \([2]\) | \(24576\) | \(1.5811\) |
Rank
sage: E.rank()
The elliptic curves in class 5850.m have rank \(1\).
Complex multiplication
The elliptic curves in class 5850.m do not have complex multiplication.Modular form 5850.2.a.m
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
