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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 46475.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46475.i1 | 46475f4 | \([1, -1, 0, -250067, 48181966]\) | \(22930509321/6875\) | \(518504873046875\) | \([2]\) | \(221184\) | \(1.8015\) | |
| 46475.i2 | 46475f3 | \([1, -1, 0, -123317, -16249284]\) | \(2749884201/73205\) | \(5521039888203125\) | \([2]\) | \(221184\) | \(1.8015\) | |
| 46475.i3 | 46475f2 | \([1, -1, 0, -17692, 545091]\) | \(8120601/3025\) | \(228142144140625\) | \([2, 2]\) | \(110592\) | \(1.4550\) | |
| 46475.i4 | 46475f1 | \([1, -1, 0, 3433, 59216]\) | \(59319/55\) | \(-4148038984375\) | \([2]\) | \(55296\) | \(1.1084\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46475.i have rank \(0\).
Complex multiplication
The elliptic curves in class 46475.i do not have complex multiplication.Modular form 46475.2.a.i
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.
