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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 1344j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1344.m4 | 1344j1 | \([0, 1, 0, -29, 387]\) | \(-2725888/64827\) | \(-66382848\) | \([2]\) | \(384\) | \(0.18162\) | \(\Gamma_0(N)\)-optimal |
| 1344.m3 | 1344j2 | \([0, 1, 0, -1009, 11951]\) | \(6940769488/35721\) | \(585252864\) | \([2, 2]\) | \(768\) | \(0.52819\) | |
| 1344.m2 | 1344j3 | \([0, 1, 0, -1569, -3393]\) | \(6522128932/3720087\) | \(243799621632\) | \([2]\) | \(1536\) | \(0.87476\) | |
| 1344.m1 | 1344j4 | \([0, 1, 0, -16129, 783071]\) | \(7080974546692/189\) | \(12386304\) | \([2]\) | \(1536\) | \(0.87476\) |
Rank
sage: E.rank()
The elliptic curves in class 1344j have rank \(1\).
Complex multiplication
The elliptic curves in class 1344j do not have complex multiplication.Modular form 1344.2.a.j
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.
