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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 496.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
496.b1 | 496f3 | \([0, 0, 0, -5291, -148134]\) | \(3999236143617/62\) | \(253952\) | \([2]\) | \(192\) | \(0.58507\) | |
496.b2 | 496f4 | \([0, 0, 0, -491, 154]\) | \(3196010817/1847042\) | \(7565484032\) | \([4]\) | \(192\) | \(0.58507\) | |
496.b3 | 496f2 | \([0, 0, 0, -331, -2310]\) | \(979146657/3844\) | \(15745024\) | \([2, 2]\) | \(96\) | \(0.23850\) | |
496.b4 | 496f1 | \([0, 0, 0, -11, -70]\) | \(-35937/496\) | \(-2031616\) | \([2]\) | \(48\) | \(-0.10808\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 496.b have rank \(1\).
Complex multiplication
The elliptic curves in class 496.b do not have complex multiplication.Modular form 496.2.a.b
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.