Show commands:
SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 44100.ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44100.ca1 | 44100bg3 | \([0, 0, 0, -455700, -118377875]\) | \(488095744/125\) | \(2680191281250000\) | \([2]\) | \(311040\) | \(1.9463\) | |
| 44100.ca2 | 44100bg4 | \([0, 0, 0, -400575, -148090250]\) | \(-20720464/15625\) | \(-5360382562500000000\) | \([2]\) | \(622080\) | \(2.2929\) | |
| 44100.ca3 | 44100bg1 | \([0, 0, 0, -14700, 471625]\) | \(16384/5\) | \(107207651250000\) | \([2]\) | \(103680\) | \(1.3970\) | \(\Gamma_0(N)\)-optimal |
| 44100.ca4 | 44100bg2 | \([0, 0, 0, 40425, 3172750]\) | \(21296/25\) | \(-8576612100000000\) | \([2]\) | \(207360\) | \(1.7436\) |
Rank
sage: E.rank()
The elliptic curves in class 44100.ca have rank \(0\).
Complex multiplication
The elliptic curves in class 44100.ca do not have complex multiplication.Modular form 44100.2.a.ca
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
