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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 14196h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14196.l4 | 14196h1 | \([0, 1, 0, 1127, -4588]\) | \(2048000/1323\) | \(-102173892912\) | \([2]\) | \(13824\) | \(0.80140\) | \(\Gamma_0(N)\)-optimal |
| 14196.l3 | 14196h2 | \([0, 1, 0, -4788, -42444]\) | \(9826000/5103\) | \(6305588819712\) | \([2]\) | \(27648\) | \(1.1480\) | |
| 14196.l2 | 14196h3 | \([0, 1, 0, -19153, -1057120]\) | \(-10061824000/352947\) | \(-27257724097968\) | \([2]\) | \(41472\) | \(1.3507\) | |
| 14196.l1 | 14196h4 | \([0, 1, 0, -308988, -66212028]\) | \(2640279346000/3087\) | \(3814492002048\) | \([2]\) | \(82944\) | \(1.6973\) |
Rank
sage: E.rank()
The elliptic curves in class 14196h have rank \(1\).
Complex multiplication
The elliptic curves in class 14196h do not have complex multiplication.Modular form 14196.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
