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SageMath
E = EllipticCurve("vt1")
E.isogeny_class()
Elliptic curves in class 369600vt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.vt1 | 369600vt1 | \([0, 1, 0, -17773, -917917]\) | \(4850878539776/130977\) | \(16765056000\) | \([2]\) | \(532480\) | \(1.0662\) | \(\Gamma_0(N)\)-optimal |
| 369600.vt2 | 369600vt2 | \([0, 1, 0, -17073, -992817]\) | \(-268750151696/50014503\) | \(-102429702144000\) | \([2]\) | \(1064960\) | \(1.4128\) |
Rank
sage: E.rank()
The elliptic curves in class 369600vt have rank \(0\).
Complex multiplication
The elliptic curves in class 369600vt do not have complex multiplication.Modular form 369600.2.a.vt
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
