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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 624.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 624.f1 | 624f3 | \([0, 1, 0, -304, 1892]\) | \(3044193988/85293\) | \(87340032\) | \([4]\) | \(256\) | \(0.30283\) | |
| 624.f2 | 624f2 | \([0, 1, 0, -44, -84]\) | \(37642192/13689\) | \(3504384\) | \([2, 2]\) | \(128\) | \(-0.043740\) | |
| 624.f3 | 624f1 | \([0, 1, 0, -39, -108]\) | \(420616192/117\) | \(1872\) | \([2]\) | \(64\) | \(-0.39031\) | \(\Gamma_0(N)\)-optimal |
| 624.f4 | 624f4 | \([0, 1, 0, 136, -444]\) | \(269676572/257049\) | \(-263218176\) | \([4]\) | \(256\) | \(0.30283\) |
Rank
sage: E.rank()
The elliptic curves in class 624.f have rank \(1\).
Complex multiplication
The elliptic curves in class 624.f do not have complex multiplication.Modular form 624.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
