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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 214245.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
214245.g1 | 214245e2 | \([1, -1, 1, -1072118, -428857118]\) | \(-15590912409/78125\) | \(-682919625746953125\) | \([]\) | \(3143448\) | \(2.2694\) | |
214245.g2 | 214245e1 | \([1, -1, 1, -893, 318466]\) | \(-9/5\) | \(-43706856047805\) | \([]\) | \(449064\) | \(1.2965\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 214245.g have rank \(1\).
Complex multiplication
The elliptic curves in class 214245.g do not have complex multiplication.Modular form 214245.2.a.g
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.