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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 1344.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1344.p1 | 1344f1 | \([0, 1, 0, -8, 6]\) | \(1000000/63\) | \(4032\) | \([2]\) | \(64\) | \(-0.55712\) | \(\Gamma_0(N)\)-optimal |
| 1344.p2 | 1344f2 | \([0, 1, 0, 7, 39]\) | \(8000/147\) | \(-602112\) | \([2]\) | \(128\) | \(-0.21054\) |
Rank
sage: E.rank()
The elliptic curves in class 1344.p have rank \(0\).
Complex multiplication
The elliptic curves in class 1344.p do not have complex multiplication.Modular form 1344.2.a.p
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
