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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 92400.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92400.v1 | 92400dm2 | \([0, -1, 0, -12908, -559188]\) | \(59466754384/121275\) | \(485100000000\) | \([2]\) | \(184320\) | \(1.1288\) | |
92400.v2 | 92400dm1 | \([0, -1, 0, -533, -14688]\) | \(-67108864/343035\) | \(-85758750000\) | \([2]\) | \(92160\) | \(0.78222\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92400.v have rank \(0\).
Complex multiplication
The elliptic curves in class 92400.v do not have complex multiplication.Modular form 92400.2.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.