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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 448e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 448.h2 | 448e1 | \([0, -1, 0, -1, 33]\) | \(-4/7\) | \(-458752\) | \([2]\) | \(64\) | \(-0.23467\) | \(\Gamma_0(N)\)-optimal |
| 448.h1 | 448e2 | \([0, -1, 0, -161, 833]\) | \(3543122/49\) | \(6422528\) | \([2]\) | \(128\) | \(0.11190\) |
Rank
sage: E.rank()
The elliptic curves in class 448e have rank \(0\).
Complex multiplication
The elliptic curves in class 448e do not have complex multiplication.Modular form 448.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
