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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 162288v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162288.cf4 | 162288v1 | \([0, 0, 0, -4226691, 5455889026]\) | \(-23771111713777/22848457968\) | \(-8026618309619311116288\) | \([2]\) | \(8847360\) | \(2.8993\) | \(\Gamma_0(N)\)-optimal |
162288.cf3 | 162288v2 | \([0, 0, 0, -78879171, 269561432770]\) | \(154502321244119857/55101928644\) | \(19357199070882488008704\) | \([2, 2]\) | \(17694720\) | \(3.2458\) | |
162288.cf1 | 162288v3 | \([0, 0, 0, -1261958691, 17255034101410]\) | \(632678989847546725777/80515134\) | \(28284808089498476544\) | \([2]\) | \(35389440\) | \(3.5924\) | |
162288.cf2 | 162288v4 | \([0, 0, 0, -90239331, 186843563746]\) | \(231331938231569617/90942310746882\) | \(31947854755990249409421312\) | \([2]\) | \(35389440\) | \(3.5924\) |
Rank
sage: E.rank()
The elliptic curves in class 162288v have rank \(1\).
Complex multiplication
The elliptic curves in class 162288v do not have complex multiplication.Modular form 162288.2.a.v
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.