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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 11760i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11760.r1 | 11760i1 | \([0, -1, 0, -856, -9344]\) | \(197723452/375\) | \(131712000\) | \([2]\) | \(7680\) | \(0.44779\) | \(\Gamma_0(N)\)-optimal |
11760.r2 | 11760i2 | \([0, -1, 0, -576, -15840]\) | \(-30138446/140625\) | \(-98784000000\) | \([2]\) | \(15360\) | \(0.79436\) |
Rank
sage: E.rank()
The elliptic curves in class 11760i have rank \(0\).
Complex multiplication
The elliptic curves in class 11760i do not have complex multiplication.Modular form 11760.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.