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SageMath
E = EllipticCurve("dt1")
E.isogeny_class()
Elliptic curves in class 187200.dt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
187200.dt1 | 187200df2 | \([0, 0, 0, -12276300, -16555718000]\) | \(68523370149961/243360\) | \(726669066240000000\) | \([2]\) | \(5898240\) | \(2.6456\) | |
187200.dt2 | 187200df1 | \([0, 0, 0, -756300, -266438000]\) | \(-16022066761/998400\) | \(-2981206425600000000\) | \([2]\) | \(2949120\) | \(2.2990\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 187200.dt have rank \(1\).
Complex multiplication
The elliptic curves in class 187200.dt do not have complex multiplication.Modular form 187200.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.