Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 14400m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality | CM discriminant |
|---|---|---|---|---|---|---|---|---|---|
| 14400.c2 | 14400m1 | \([0, 0, 0, 0, 10]\) | \(0\) | \(-43200\) | \([]\) | \(1152\) | \(-0.43165\) | \(\Gamma_0(N)\)-optimal | \(-3\) |
| 14400.c1 | 14400m2 | \([0, 0, 0, 0, -270]\) | \(0\) | \(-31492800\) | \([]\) | \(3456\) | \(0.11766\) | \(-3\) |
Rank
sage: E.rank()
The elliptic curves in class 14400m have rank \(1\).
Complex multiplication
Each elliptic curve in class 14400m has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).Modular form 14400.2.a.m
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.
