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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 11310i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11310.i4 | 11310i1 | \([1, 1, 1, 34515, 4248915]\) | \(4547226203385942959/10377808593750000\) | \(-10377808593750000\) | \([4]\) | \(103680\) | \(1.7573\) | \(\Gamma_0(N)\)-optimal |
11310.i3 | 11310i2 | \([1, 1, 1, -277985, 46373915]\) | \(2375679751819859057041/441134740310062500\) | \(441134740310062500\) | \([2, 2]\) | \(207360\) | \(2.1039\) | |
11310.i2 | 11310i3 | \([1, 1, 1, -1329235, -547792585]\) | \(259734139401368855237041/20937966860481050250\) | \(20937966860481050250\) | \([2]\) | \(414720\) | \(2.4504\) | |
11310.i1 | 11310i4 | \([1, 1, 1, -4226735, 3342790415]\) | \(8351005675201800382877041/395069604635949750\) | \(395069604635949750\) | \([2]\) | \(414720\) | \(2.4504\) |
Rank
sage: E.rank()
The elliptic curves in class 11310i have rank \(0\).
Complex multiplication
The elliptic curves in class 11310i do not have complex multiplication.Modular form 11310.2.a.i
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.