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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 1344q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1344.l3 | 1344q1 | \([0, 1, 0, -84, 270]\) | \(1036433728/63\) | \(4032\) | \([2]\) | \(128\) | \(-0.24763\) | \(\Gamma_0(N)\)-optimal |
| 1344.l2 | 1344q2 | \([0, 1, 0, -89, 231]\) | \(19248832/3969\) | \(16257024\) | \([2, 2]\) | \(256\) | \(0.098947\) | |
| 1344.l1 | 1344q3 | \([0, 1, 0, -449, -3585]\) | \(306182024/21609\) | \(708083712\) | \([2]\) | \(512\) | \(0.44552\) | |
| 1344.l4 | 1344q4 | \([0, 1, 0, 191, 1631]\) | \(23393656/45927\) | \(-1504935936\) | \([4]\) | \(512\) | \(0.44552\) |
Rank
sage: E.rank()
The elliptic curves in class 1344q have rank \(1\).
Complex multiplication
The elliptic curves in class 1344q do not have complex multiplication.Modular form 1344.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
