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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 320790.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
320790.b1 | 320790b2 | \([1, 1, 0, -59742808, -144682119488]\) | \(976983184602237747241/190867691250000000\) | \(4607082067417571250000000\) | \([2]\) | \(72253440\) | \(3.4492\) | |
320790.b2 | 320790b1 | \([1, 1, 0, -56598488, -163907120832]\) | \(830700905764449966121/44346009600000\) | \(1070404866594662400000\) | \([2]\) | \(36126720\) | \(3.1027\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 320790.b have rank \(0\).
Complex multiplication
The elliptic curves in class 320790.b do not have complex multiplication.Modular form 320790.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.