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SageMath
E = EllipticCurve("dt1")
E.isogeny_class()
Elliptic curves in class 121275dt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121275.dw1 | 121275dt1 | \([0, 0, 1, -10290, 421461]\) | \(-56197120/3267\) | \(-7004947932675\) | \([]\) | \(217728\) | \(1.2211\) | \(\Gamma_0(N)\)-optimal |
| 121275.dw2 | 121275dt2 | \([0, 0, 1, 55860, 745596]\) | \(8990228480/5314683\) | \(-11395493631366075\) | \([]\) | \(653184\) | \(1.7704\) |
Rank
sage: E.rank()
The elliptic curves in class 121275dt have rank \(0\).
Complex multiplication
The elliptic curves in class 121275dt do not have complex multiplication.Modular form 121275.2.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 Cremona 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 Cremona labels.
