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SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 333270.du
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
333270.du1 | 333270du2 | \([1, -1, 1, -74320103, -246561106913]\) | \(420676324562824569/56350000000\) | \(6081188489614350000000\) | \([2]\) | \(45416448\) | \(3.1990\) | |
333270.du2 | 333270du1 | \([1, -1, 1, -4238183, -4554220769]\) | \(-78013216986489/37918720000\) | \(-4092118608782776320000\) | \([2]\) | \(22708224\) | \(2.8524\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 333270.du have rank \(1\).
Complex multiplication
The elliptic curves in class 333270.du do not have complex multiplication.Modular form 333270.2.a.du
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.