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SageMath
E = EllipticCurve("ew1")
E.isogeny_class()
Elliptic curves in class 444675ew
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 444675.ew2 | 444675ew1 | \([0, 1, 1, -8983, 97444]\) | \(360448/189\) | \(42039296578125\) | \([]\) | \(995328\) | \(1.3059\) | \(\Gamma_0(N)\)-optimal |
| 444675.ew1 | 444675ew2 | \([0, 1, 1, -413233, -102379931]\) | \(35084566528/1029\) | \(228880614703125\) | \([]\) | \(2985984\) | \(1.8552\) |
Rank
sage: E.rank()
The elliptic curves in class 444675ew have rank \(0\).
Complex multiplication
The elliptic curves in class 444675ew do not have complex multiplication.Modular form 444675.2.a.ew
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
