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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 94640h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 94640.h2 | 94640h1 | \([0, 1, 0, -2575616, 1529721220]\) | \(174011157652/7503125\) | \(81476489582633600000\) | \([2]\) | \(3194880\) | \(2.5844\) | \(\Gamma_0(N)\)-optimal |
| 94640.h1 | 94640h2 | \([0, 1, 0, -6881736, -4924291436]\) | \(1659578027546/478515625\) | \(10392409385540000000000\) | \([2]\) | \(6389760\) | \(2.9310\) |
Rank
sage: E.rank()
The elliptic curves in class 94640h have rank \(0\).
Complex multiplication
The elliptic curves in class 94640h do not have complex multiplication.Modular form 94640.2.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 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.
