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SageMath
E = EllipticCurve("eh1")
E.isogeny_class()
Elliptic curves in class 68544.eh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 68544.eh1 | 68544cl4 | \([0, 0, 0, -45804, -3773072]\) | \(444893916104/9639\) | \(230255198208\) | \([2]\) | \(114688\) | \(1.2966\) | |
| 68544.eh2 | 68544cl2 | \([0, 0, 0, -2964, -54560]\) | \(964430272/127449\) | \(380560674816\) | \([2, 2]\) | \(57344\) | \(0.95002\) | |
| 68544.eh3 | 68544cl1 | \([0, 0, 0, -759, 7180]\) | \(1036433728/122451\) | \(5713073856\) | \([2]\) | \(28672\) | \(0.60345\) | \(\Gamma_0(N)\)-optimal |
| 68544.eh4 | 68544cl3 | \([0, 0, 0, 4596, -287408]\) | \(449455096/1753941\) | \(-41897918103552\) | \([2]\) | \(114688\) | \(1.2966\) |
Rank
sage: E.rank()
The elliptic curves in class 68544.eh have rank \(0\).
Complex multiplication
The elliptic curves in class 68544.eh do not have complex multiplication.Modular form 68544.2.a.eh
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
