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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 22848.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22848.f1 | 22848bz4 | \([0, -1, 0, -169729, 26970433]\) | \(16502300582616584/331494849\) | \(10862423212032\) | \([4]\) | \(114688\) | \(1.6219\) | |
| 22848.f2 | 22848bz3 | \([0, -1, 0, -44289, -3171231]\) | \(293204888234504/35857918593\) | \(1174992276455424\) | \([2]\) | \(114688\) | \(1.6219\) | |
| 22848.f3 | 22848bz2 | \([0, -1, 0, -10969, 394009]\) | \(35637273157312/4552605729\) | \(18647473065984\) | \([2, 2]\) | \(57344\) | \(1.2753\) | |
| 22848.f4 | 22848bz1 | \([0, -1, 0, 1036, 31458]\) | \(1919569026752/7938130977\) | \(-508040382528\) | \([2]\) | \(28672\) | \(0.92877\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22848.f have rank \(1\).
Complex multiplication
The elliptic curves in class 22848.f do not have complex multiplication.Modular form 22848.2.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.
