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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 5445.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5445.i1 | 5445e4 | \([1, -1, 0, -64455, 6312950]\) | \(22930509321/6875\) | \(8878842286875\) | \([2]\) | \(15360\) | \(1.4626\) | |
5445.i2 | 5445e3 | \([1, -1, 0, -31785, -2122444]\) | \(2749884201/73205\) | \(94541912670645\) | \([2]\) | \(15360\) | \(1.4626\) | |
5445.i3 | 5445e2 | \([1, -1, 0, -4560, 71891]\) | \(8120601/3025\) | \(3906690606225\) | \([2, 2]\) | \(7680\) | \(1.1160\) | |
5445.i4 | 5445e1 | \([1, -1, 0, 885, 7640]\) | \(59319/55\) | \(-71030738295\) | \([2]\) | \(3840\) | \(0.76944\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5445.i have rank \(1\).
Complex multiplication
The elliptic curves in class 5445.i do not have complex multiplication.Modular form 5445.2.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.