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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 112710g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
112710.e2 | 112710g1 | \([1, 1, 0, -84538, -10693358]\) | \(-2768178670921/431115750\) | \(-10406086162611750\) | \([]\) | \(995328\) | \(1.8021\) | \(\Gamma_0(N)\)-optimal |
112710.e1 | 112710g2 | \([1, 1, 0, -7085563, -7262502443]\) | \(-1629871520330191321/4481880\) | \(-108181687749720\) | \([]\) | \(2985984\) | \(2.3514\) |
Rank
sage: E.rank()
The elliptic curves in class 112710g have rank \(0\).
Complex multiplication
The elliptic curves in class 112710g do not have complex multiplication.Modular form 112710.2.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 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.