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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 463680e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
463680.e1 | 463680e1 | \([0, 0, 0, -17148, -863728]\) | \(46689225424/36225\) | \(432669081600\) | \([2]\) | \(1048576\) | \(1.1642\) | \(\Gamma_0(N)\)-optimal |
463680.e2 | 463680e2 | \([0, 0, 0, -13548, -1236688]\) | \(-5756278756/10498005\) | \(-501549999390720\) | \([2]\) | \(2097152\) | \(1.5108\) |
Rank
sage: E.rank()
The elliptic curves in class 463680e have rank \(0\).
Complex multiplication
The elliptic curves in class 463680e do not have complex multiplication.Modular form 463680.2.a.e
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.