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SageMath
E = EllipticCurve("ec1")
E.isogeny_class()
Elliptic curves in class 176400ec
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176400.da2 | 176400ec1 | \([0, 0, 0, -255675, 58518250]\) | \(-115501303/25600\) | \(-409677004800000000\) | \([2]\) | \(2211840\) | \(2.1000\) | \(\Gamma_0(N)\)-optimal |
176400.da1 | 176400ec2 | \([0, 0, 0, -4287675, 3417174250]\) | \(544737993463/20000\) | \(320060160000000000\) | \([2]\) | \(4423680\) | \(2.4465\) |
Rank
sage: E.rank()
The elliptic curves in class 176400ec have rank \(0\).
Complex multiplication
The elliptic curves in class 176400ec do not have complex multiplication.Modular form 176400.2.a.ec
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.