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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 29400.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29400.bb1 | 29400cp4 | \([0, -1, 0, -4577008, 3770470012]\) | \(5633270409316/14175\) | \(26682793200000000\) | \([2]\) | \(589824\) | \(2.3901\) | |
29400.bb2 | 29400cp3 | \([0, -1, 0, -804008, -202841988]\) | \(30534944836/8203125\) | \(15441431250000000000\) | \([2]\) | \(589824\) | \(2.3901\) | |
29400.bb3 | 29400cp2 | \([0, -1, 0, -289508, 57495012]\) | \(5702413264/275625\) | \(129708022500000000\) | \([2, 2]\) | \(294912\) | \(2.0436\) | |
29400.bb4 | 29400cp1 | \([0, -1, 0, 10617, 3472512]\) | \(4499456/180075\) | \(-5296410918750000\) | \([2]\) | \(147456\) | \(1.6970\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29400.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 29400.bb do not have complex multiplication.Modular form 29400.2.a.bb
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.