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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 5040.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5040.v1 | 5040bk3 | \([0, 0, 0, -18912, -1047184]\) | \(-250523582464/13671875\) | \(-40824000000000\) | \([]\) | \(12960\) | \(1.3699\) | |
5040.v2 | 5040bk1 | \([0, 0, 0, -192, 1136]\) | \(-262144/35\) | \(-104509440\) | \([]\) | \(1440\) | \(0.27130\) | \(\Gamma_0(N)\)-optimal |
5040.v3 | 5040bk2 | \([0, 0, 0, 1248, -2896]\) | \(71991296/42875\) | \(-128024064000\) | \([]\) | \(4320\) | \(0.82061\) |
Rank
sage: E.rank()
The elliptic curves in class 5040.v have rank \(0\).
Complex multiplication
The elliptic curves in class 5040.v do not have complex multiplication.Modular form 5040.2.a.v
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.