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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 1440.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1440.h1 | 1440i2 | \([0, 0, 0, -27, 46]\) | \(157464/25\) | \(345600\) | \([2]\) | \(128\) | \(-0.21464\) | |
| 1440.h2 | 1440i1 | \([0, 0, 0, 3, 4]\) | \(1728/5\) | \(-8640\) | \([2]\) | \(64\) | \(-0.56121\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1440.h have rank \(1\).
Complex multiplication
The elliptic curves in class 1440.h do not have complex multiplication.Modular form 1440.2.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.
