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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 14400.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14400.z1 | 14400cm1 | \([0, 0, 0, -300, 2050]\) | \(-102400/3\) | \(-87480000\) | \([]\) | \(3840\) | \(0.30278\) | \(\Gamma_0(N)\)-optimal |
| 14400.z2 | 14400cm2 | \([0, 0, 0, 1500, -98750]\) | \(20480/243\) | \(-4428675000000\) | \([]\) | \(19200\) | \(1.1075\) |
Rank
sage: E.rank()
The elliptic curves in class 14400.z have rank \(1\).
Complex multiplication
The elliptic curves in class 14400.z do not have complex multiplication.Modular form 14400.2.a.z
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
