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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 28611c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28611.h1 | 28611c1 | \([1, -1, 1, -172154, 18286696]\) | \(1187648379/384659\) | \(182751402669611193\) | \([2]\) | \(248832\) | \(2.0156\) | \(\Gamma_0(N)\)-optimal |
| 28611.h2 | 28611c2 | \([1, -1, 1, 491101, 124672798]\) | \(27570978261/30116537\) | \(-14308359820779558699\) | \([2]\) | \(497664\) | \(2.3622\) |
Rank
sage: E.rank()
The elliptic curves in class 28611c have rank \(1\).
Complex multiplication
The elliptic curves in class 28611c do not have complex multiplication.Modular form 28611.2.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 Cremona 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 Cremona labels.
