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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 30960.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30960.bb1 | 30960bc2 | \([0, 0, 0, -180000387, -929519000766]\) | \(8000051600110940079507/144453125\) | \(11646037440000000\) | \([2]\) | \(3440640\) | \(3.0737\) | |
30960.bb2 | 30960bc1 | \([0, 0, 0, -11250387, -14522750766]\) | \(1953326569433829507/262451171875\) | \(21159225000000000000\) | \([2]\) | \(1720320\) | \(2.7271\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30960.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 30960.bb do not have complex multiplication.Modular form 30960.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.