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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 672.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 672.h1 | 672h2 | \([0, 1, 0, -337, -2497]\) | \(1036433728/63\) | \(258048\) | \([2]\) | \(128\) | \(0.098947\) | |
| 672.h2 | 672h3 | \([0, 1, 0, -112, 392]\) | \(306182024/21609\) | \(11063808\) | \([4]\) | \(128\) | \(0.098947\) | |
| 672.h3 | 672h1 | \([0, 1, 0, -22, -40]\) | \(19248832/3969\) | \(254016\) | \([2, 2]\) | \(64\) | \(-0.24763\) | \(\Gamma_0(N)\)-optimal |
| 672.h4 | 672h4 | \([0, 1, 0, 48, -180]\) | \(23393656/45927\) | \(-23514624\) | \([2]\) | \(128\) | \(0.098947\) |
Rank
sage: E.rank()
The elliptic curves in class 672.h have rank \(0\).
Complex multiplication
The elliptic curves in class 672.h do not have complex multiplication.Modular form 672.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
