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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 310464.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
310464.bb1 | 310464bb1 | \([0, 0, 0, -157584, 24077914]\) | \(-78843215872/539\) | \(-2958588110016\) | \([]\) | \(1382400\) | \(1.5738\) | \(\Gamma_0(N)\)-optimal |
310464.bb2 | 310464bb2 | \([0, 0, 0, -87024, 45686914]\) | \(-13278380032/156590819\) | \(-859531976309958336\) | \([]\) | \(4147200\) | \(2.1231\) | |
310464.bb3 | 310464bb3 | \([0, 0, 0, 777336, -1182568646]\) | \(9463555063808/115539436859\) | \(-634199636602934652096\) | \([]\) | \(12441600\) | \(2.6724\) |
Rank
sage: E.rank()
The elliptic curves in class 310464.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 310464.bb do not have complex multiplication.Modular form 310464.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.