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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 3120.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3120.h1 | 3120c3 | \([0, -1, 0, -1656, 26400]\) | \(490757540836/2142075\) | \(2193484800\) | \([4]\) | \(3072\) | \(0.64532\) | |
| 3120.h2 | 3120c2 | \([0, -1, 0, -156, 0]\) | \(1650587344/950625\) | \(243360000\) | \([2, 2]\) | \(1536\) | \(0.29875\) | |
| 3120.h3 | 3120c1 | \([0, -1, 0, -111, -414]\) | \(9538484224/26325\) | \(421200\) | \([2]\) | \(768\) | \(-0.047827\) | \(\Gamma_0(N)\)-optimal |
| 3120.h4 | 3120c4 | \([0, -1, 0, 624, -624]\) | \(26198797244/15234375\) | \(-15600000000\) | \([2]\) | \(3072\) | \(0.64532\) |
Rank
sage: E.rank()
The elliptic curves in class 3120.h have rank \(0\).
Complex multiplication
The elliptic curves in class 3120.h do not have complex multiplication.Modular form 3120.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
