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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 93138.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
93138.v1 | 93138x2 | \([1, 1, 1, -11800195, 13661186621]\) | \(563130251390539/75856356588\) | \(24477913069284599618052\) | \([2]\) | \(19553280\) | \(3.0234\) | |
93138.v2 | 93138x1 | \([1, 1, 1, -11388655, 14787983141]\) | \(506242516969099/11449008\) | \(3694454033373353232\) | \([2]\) | \(9776640\) | \(2.6768\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 93138.v have rank \(0\).
Complex multiplication
The elliptic curves in class 93138.v do not have complex multiplication.Modular form 93138.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.