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SageMath
E = EllipticCurve("wt1")
E.isogeny_class()
Elliptic curves in class 6350400.wt
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 6350400.wt1 | \([0, 0, 0, -17654700, -28675486000]\) | \(-15590912409/78125\) | \(-3049462080000000000000\) | \([]\) | \(340623360\) | \(2.9698\) |
| 6350400.wt2 | \([0, 0, 0, -14700, 21266000]\) | \(-9/5\) | \(-195165573120000000\) | \([]\) | \(48660480\) | \(1.9968\) |
Rank
sage: E.rank()
The elliptic curves in class 6350400.wt have rank \(1\).
Complex multiplication
The elliptic curves in class 6350400.wt do not have complex multiplication.Modular form 6350400.2.a.wt
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
