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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 12168c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12168.o1 | 12168c1 | \([0, 0, 0, -5070, 63713]\) | \(256000/117\) | \(6587088320592\) | \([2]\) | \(21504\) | \(1.1546\) | \(\Gamma_0(N)\)-optimal |
| 12168.o2 | 12168c2 | \([0, 0, 0, 17745, 478946]\) | \(686000/507\) | \(-456704790227712\) | \([2]\) | \(43008\) | \(1.5012\) |
Rank
sage: E.rank()
The elliptic curves in class 12168c have rank \(0\).
Complex multiplication
The elliptic curves in class 12168c do not have complex multiplication.Modular form 12168.2.a.c
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.
