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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 24150.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24150.p1 | 24150m4 | \([1, 1, 0, -10819525, 13693595125]\) | \(8964546681033941529169/31696875000\) | \(495263671875000\) | \([2]\) | \(884736\) | \(2.4620\) | |
24150.p2 | 24150m3 | \([1, 1, 0, -901525, 58973125]\) | \(5186062692284555089/2903809817953800\) | \(45372028405528125000\) | \([2]\) | \(884736\) | \(2.4620\) | |
24150.p3 | 24150m2 | \([1, 1, 0, -676525, 213548125]\) | \(2191574502231419089/4115217960000\) | \(64300280625000000\) | \([2, 2]\) | \(442368\) | \(2.1154\) | |
24150.p4 | 24150m1 | \([1, 1, 0, -28525, 5540125]\) | \(-164287467238609/757170892800\) | \(-11830795200000000\) | \([2]\) | \(221184\) | \(1.7689\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 24150.p have rank \(1\).
Complex multiplication
The elliptic curves in class 24150.p do not have complex multiplication.Modular form 24150.2.a.p
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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.