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SageMath
E = EllipticCurve("ev1")
E.isogeny_class()
Elliptic curves in class 444675ev
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
444675.ev2 | 444675ev1 | \([0, 1, 1, -197633, -1959881731]\) | \(-262144/509355\) | \(-1658765334534884296875\) | \([]\) | \(19906560\) | \(2.7507\) | \(\Gamma_0(N)\)-optimal |
444675.ev1 | 444675ev2 | \([0, 1, 1, -124706633, -536087928106]\) | \(-65860951343104/3493875\) | \(-11378152238022732421875\) | \([]\) | \(59719680\) | \(3.3000\) |
Rank
sage: E.rank()
The elliptic curves in class 444675ev have rank \(0\).
Complex multiplication
The elliptic curves in class 444675ev do not have complex multiplication.Modular form 444675.2.a.ev
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.