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SageMath
E = EllipticCurve("ef1")
E.isogeny_class()
Elliptic curves in class 14400.ef
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14400.ef1 | 14400dy4 | \([0, 0, 0, -1807500, -935350000]\) | \(-349938025/8\) | \(-14929920000000000\) | \([]\) | \(172800\) | \(2.2170\) | |
| 14400.ef2 | 14400dy3 | \([0, 0, 0, -7500, -2950000]\) | \(-25/2\) | \(-3732480000000000\) | \([]\) | \(57600\) | \(1.6676\) | |
| 14400.ef3 | 14400dy1 | \([0, 0, 0, -1740, 33680]\) | \(-121945/32\) | \(-152882380800\) | \([]\) | \(11520\) | \(0.86293\) | \(\Gamma_0(N)\)-optimal |
| 14400.ef4 | 14400dy2 | \([0, 0, 0, 12660, -248560]\) | \(46969655/32768\) | \(-156551557939200\) | \([]\) | \(34560\) | \(1.4122\) |
Rank
sage: E.rank()
The elliptic curves in class 14400.ef have rank \(1\).
Complex multiplication
The elliptic curves in class 14400.ef do not have complex multiplication.Modular form 14400.2.a.ef
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 15 & 5 \\ 3 & 1 & 5 & 15 \\ 15 & 5 & 1 & 3 \\ 5 & 15 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
