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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 54390m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54390.l2 | 54390m1 | \([1, 1, 0, 2033, 155611]\) | \(7892485271/92517390\) | \(-10884578416110\) | \([]\) | \(152064\) | \(1.1825\) | \(\Gamma_0(N)\)-optimal |
54390.l1 | 54390m2 | \([1, 1, 0, -167752, 26392024]\) | \(-4437543642183289/3191139000\) | \(-375434312211000\) | \([]\) | \(456192\) | \(1.7318\) |
Rank
sage: E.rank()
The elliptic curves in class 54390m have rank \(2\).
Complex multiplication
The elliptic curves in class 54390m do not have complex multiplication.Modular form 54390.2.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 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.