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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 22320.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22320.c1 | 22320bl2 | \([0, 0, 0, -31456443, 67906685162]\) | \(1152829477932246539641/3188367360\) | \(9520413923082240\) | \([2]\) | \(798720\) | \(2.7242\) | |
| 22320.c2 | 22320bl1 | \([0, 0, 0, -1965243, 1061931242]\) | \(-281115640967896441/468084326400\) | \(-1397692309281177600\) | \([2]\) | \(399360\) | \(2.3776\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22320.c have rank \(1\).
Complex multiplication
The elliptic curves in class 22320.c do not have complex multiplication.Modular form 22320.2.a.c
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
