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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 59850.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59850.m1 | 59850l2 | \([1, -1, 0, -165417, -30594259]\) | \(-1627624771947/376421920\) | \(-115767385177500000\) | \([]\) | \(622080\) | \(1.9937\) | |
| 59850.m2 | 59850l1 | \([1, -1, 0, 14583, 265741]\) | \(812949929037/544768000\) | \(-229824000000000\) | \([]\) | \(207360\) | \(1.4444\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 59850.m have rank \(0\).
Complex multiplication
The elliptic curves in class 59850.m do not have complex multiplication.Modular form 59850.2.a.m
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
