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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 194922h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 194922.dg3 | 194922h1 | \([1, -1, 1, -384341, 91806621]\) | \(73207745356537/668304\) | \(57317841728784\) | \([4]\) | \(1474560\) | \(1.8045\) | \(\Gamma_0(N)\)-optimal |
| 194922.dg2 | 194922h2 | \([1, -1, 1, -393161, 87378981]\) | \(78364289651257/6978597444\) | \(598527232792394724\) | \([2, 2]\) | \(2949120\) | \(2.1511\) | |
| 194922.dg4 | 194922h3 | \([1, -1, 1, 440329, 407772537]\) | \(110088190986983/901697560218\) | \(-77335102055061774378\) | \([2]\) | \(5898240\) | \(2.4976\) | |
| 194922.dg1 | 194922h4 | \([1, -1, 1, -1367771, -516489375]\) | \(3299497626614617/563987509722\) | \(48371021001305728362\) | \([2]\) | \(5898240\) | \(2.4976\) |
Rank
sage: E.rank()
The elliptic curves in class 194922h have rank \(0\).
Complex multiplication
The elliptic curves in class 194922h do not have complex multiplication.Modular form 194922.2.a.h
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
