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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 14784bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14784.l2 | 14784bo1 | \([0, -1, 0, -33, 1089]\) | \(-62500/7623\) | \(-499580928\) | \([2]\) | \(6144\) | \(0.34857\) | \(\Gamma_0(N)\)-optimal |
14784.l1 | 14784bo2 | \([0, -1, 0, -1793, 29601]\) | \(4866277250/43659\) | \(5722472448\) | \([2]\) | \(12288\) | \(0.69514\) |
Rank
sage: E.rank()
The elliptic curves in class 14784bo have rank \(2\).
Complex multiplication
The elliptic curves in class 14784bo do not have complex multiplication.Modular form 14784.2.a.bo
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 Cremona 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 Cremona labels.