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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 11025.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11025.h1 | 11025i2 | \([1, -1, 1, -1837730, 686460772]\) | \(55306341/15625\) | \(193916026997314453125\) | \([2]\) | \(387072\) | \(2.5997\) | |
| 11025.h2 | 11025i1 | \([1, -1, 1, -680105, -207225728]\) | \(2803221/125\) | \(1551328215978515625\) | \([2]\) | \(193536\) | \(2.2531\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11025.h have rank \(0\).
Complex multiplication
The elliptic curves in class 11025.h do not have complex multiplication.Modular form 11025.2.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 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.
