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SageMath
E = EllipticCurve("dt1")
E.isogeny_class()
Elliptic curves in class 87120.dt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
87120.dt1 | 87120gc1 | \([0, 0, 0, -115797, 15797639]\) | \(-68679424/3375\) | \(-8438451709446000\) | \([]\) | \(456192\) | \(1.8175\) | \(\Gamma_0(N)\)-optimal |
87120.dt2 | 87120gc2 | \([0, 0, 0, 602943, 37934831]\) | \(9695350016/5859375\) | \(-14650089773343750000\) | \([]\) | \(1368576\) | \(2.3668\) |
Rank
sage: E.rank()
The elliptic curves in class 87120.dt have rank \(1\).
Complex multiplication
The elliptic curves in class 87120.dt do not have complex multiplication.Modular form 87120.2.a.dt
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.