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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 59840.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59840.m1 | 59840bc1 | \([0, -1, 0, -156149441, -751839987359]\) | \(-1606220241149825308027441/2128704136908800000\) | \(-558027017265820467200000\) | \([]\) | \(9216000\) | \(3.4629\) | \(\Gamma_0(N)\)-optimal |
| 59840.m2 | 59840bc2 | \([0, -1, 0, 1106148159, 8779695554401]\) | \(570983676137286216962798159/457469996554140806256680\) | \(-119923014776688687515351121920\) | \([]\) | \(46080000\) | \(4.2676\) |
Rank
sage: E.rank()
The elliptic curves in class 59840.m have rank \(0\).
Complex multiplication
The elliptic curves in class 59840.m do not have complex multiplication.Modular form 59840.2.a.m
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
