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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 21675.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
21675.bb1 | 21675z1 | \([0, 1, 1, -2408, -47431]\) | \(-102400/3\) | \(-45257941875\) | \([]\) | \(30720\) | \(0.82351\) | \(\Gamma_0(N)\)-optimal |
21675.bb2 | 21675z2 | \([0, 1, 1, 12042, 2250119]\) | \(20480/243\) | \(-2291183307421875\) | \([]\) | \(153600\) | \(1.6282\) |
Rank
sage: E.rank()
The elliptic curves in class 21675.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 21675.bb do not have complex multiplication.Modular form 21675.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.