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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 23120bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23120.u1 | 23120bc1 | \([0, 0, 0, -8092, -280041]\) | \(151732224/85\) | \(32827093840\) | \([2]\) | \(27648\) | \(0.96506\) | \(\Gamma_0(N)\)-optimal |
23120.u2 | 23120bc2 | \([0, 0, 0, -6647, -383214]\) | \(-5256144/7225\) | \(-44644847622400\) | \([2]\) | \(55296\) | \(1.3116\) |
Rank
sage: E.rank()
The elliptic curves in class 23120bc have rank \(1\).
Complex multiplication
The elliptic curves in class 23120bc do not have complex multiplication.Modular form 23120.2.a.bc
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.