Show commands:
SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 226512ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 226512.en1 | 226512ch1 | \([0, 0, 0, -100613163387, -12296788979154262]\) | \(-21293376668673906679951249/26211168887701209984\) | \(-138653225158719368138256394223616\) | \([]\) | \(812851200\) | \(5.0772\) | \(\Gamma_0(N)\)-optimal |
| 226512.en2 | 226512ch2 | \([0, 0, 0, 284936222373, 771741325057955978]\) | \(483641001192506212470106511/48918776756543177755473774\) | \(-258773128248267674569390872742072344576\) | \([]\) | \(5689958400\) | \(6.0502\) |
Rank
sage: E.rank()
The elliptic curves in class 226512ch have rank \(1\).
Complex multiplication
The elliptic curves in class 226512ch do not have complex multiplication.Modular form 226512.2.a.ch
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
